cruciate ligament forces between short and long step forward lunge
TRANSCRIPT
-
8/10/2019 Cruciate Ligament Forces Between Short and Long Step Forward Lunge
1/11
Cruciate
Ligament
Forces
between
Short-Step
and
Long-Step
Forward
Lunge
RAFAEL
F. ESCAMILLAt,
NAIQUAN
ZHENG
2
,
TORAN
D.
MACLEOD
3
,
RODNEY
IMAMURA
4
,
W.
BRENT
EDWARDS
5
, ALAN
HRELJAC
4
,
GLENN
S. FLEISIG
6
, KEVIN
E.
WILK7,
CLAUDE
T.
MOORMAN
III ,
LONNIE
PAULOS ,
and
JAMES
R.
ANDREWS
6
Andrews-Paulos
Research
andEducation
nstitute,
GulfBreeze,
FL;
2
Department
ofMechanical
Engineering
and
Engineering
Science,
The
Center
or Biomedical
Engineering,
University
ofNorth
Carolina
at Charlotte,
NC;
3
Department
ofPhysical
Therapy,
Center
or Biomedical
Engineering
Research,
University
ofDelaivare,
Newark,
DE;
4
Kinesiology
and
HealthScience
Department,
California
State
University
Sacramento,
CA;
5
Department
ofKinesiology
andNutrition,
University
of Illinois
at Chicago,
IL;
6
American
Sports
Medicine
Institute,
Birmingham,
AL;
7
Champion
Sports
Medicine,
Birmingham,
L
8
Duke University
MedicalCenter;
Durham,
NC
ABSTRACT
ESCAMILLA,
IL F.,N. ZHENG,
T.
D. MACLEOD,
R
IMAMURA,
W.
B.
EDWARDS,
A.
HRELJAC,
G.
S.
FLEISIG,
K. E.
WILK,
C.
T. MOORMAN
III,
L. PAULOS,
and
J. IR
ANDREWS.
Cmuciate Ligament
Forces
between
Short-Step
and
Long-Step
Forward
Lunge.
Med. Sci. Sports
Exerc. Vol. 42,
No.
10,
pp.
1932-1942,
2010. Purpose:
The
purpose
of this
study
was to
compare
cruciate ligament
forces
between
the
forward
lunge
with a
short step
(forward
lunge short)
and
the forward
lunge
with a
long
step (forward
lunge
long).
Methods:
Eighteen
subjects
used their
12-repetition
maximum
weight
while performing
the
forward
lunge
short and
long
with and
without a
stride.
EMG,
force,
and
kinematic
variables
were
input into a
biomechanical
model
using
optimization,
and
cruciate liga-
ment
forces
were
calculated
as
a
function
of knee
angle.
A
two-factor
repeated-measure
ANOVA
was
used
with
a
Bonferroni
adjustment
P
< 0.0025)
to assess
differences
in
cruciate forces
between
lunging
techniques.
Results:
Mean posterior
cruciate
ligament (PCL)
forces
(69-765
N
range)
were
significantly
greater
(P
< 0.001)
in the forward
lunge
long
compared
with
the forward
lunge
short
between
00 and
800
knee flexion
angles.
Mean
PCL
forces
(86-691
N
range)
were
significantly
greater
(P
< 0.001)
without
a stride
compared
with
those
with a
stride
between 00
and
20'
knee flexion
angles. Mean
anterior
cruciate
ligament
(ACL)
forces
were
generated
(0-50
N range
between 0
and
100 knee
flexion
angles)
only
in
the forward
lunge
short
with stride.
Conclusions:
All
lunge
variations
appear
appro-
priate and
safe during
ACL
rehabilitation
because
of
minimal
ACL
loading.
ACL loading
occurred
only in
the forward
lunge
short
with stride.
Clinicians
should
be cautious
in
prescribing
forward
lunge
exercises
during
early
phases
of
PCL
rehabilitation,
especially
at
higher
knee
flexion
angles
and during
the forward
lunge
long, which
generated
the
highest
PCL
forces.
Understanding
how
varying
lunging
techniques
affect
cruciate
ligament
loading
may
help clinicians
prescribe
lunging
exercises
in a
safe manner
during
ACL
and
PCL
rehabilitation.
Key
Words:
ACL, PCL, KNEE
KINETICS, REHABILITATION, CLOSED CHAIN
losed
chain
weight-bearing
exercises
such as
the
squat,
leg
press,
and
forward
lunge
are
commonly
used
in rehabilitation
settings,
such
as
after
anterior
cruciate
ligament
(ACL)
or
posterior
cruciate
ligament
(PCL)
reconstruction
surgery
(10,39).
These
exercises
can
be per-
formed
with technique
variations,
which
may
affect
ACL
and
PCL
loading.
Although
the
effects
of
exercise
technique
variations
on cruciate
ligament
loading
have
been
examined
while
performing
the squat
and
the leg press
(13,14),
there
are
Address
for correspondence:
Rafael
F.
Escamilla,
PILD.,
P.T.,
CSCS,
FACSM,
Director
of
Research,
Andrews-Paulos
Research
and
Education
Institute,
1020
Gulf
Breeze
Parkway,
Gulf
Breeze,
FL 32561;
E-mail:
Submitted
for
publication
November
2008.
Accepted
for publication
December
2009.
0195-9131/10/4210-1932/0
MEDICINE
&
SCIENCE
IN
SPORTS
&
EXERCISFO
Copyright
2010
by the
American
College of
Sports
Medicine
DOI:
10.12491MSS.0b013e3181d966d4
no studies
that have examined
the
effects of technique var-
iations
on
cruciate
ligament
loading
while
performing
the
forward
lunge.
Because
patients
use
the
forward
lunge
after
ACL
and PCL
reconstruction,
it
is
important
to
understand
how
the
cruciate
ligaments
are
loaded,
especially
during
the
early
phases
of
rehabilitation
when
the
goal
is
to
minimize
ACL
or
PCL
loading.
There
are
multiple
techniques
that individuals
can
use
during
the forward
lunge,
such
as
lunging
using
a sbort
step
length
or a
long
step
length.
Lunging
forward
using a
long
step
typically
results
in the
lead knee
being maintained over
the
lead
foot
throughout
the knee
range
of
motion,
whereas
lunging
forward
using a
short
step
length
lunge
typically
results in
the
lead knee
translating
beyond
the toes
throughout
much
of
the knee
range
of
motion.
Some
clinicians
believe
that
anterior
movement
of the
lead
knee
beyond
the toes
dur-
ing a
short step
forward
lunge
increases
cruciate ligament
loading,
although
there are very
limited
data
that support
this
belief
(2).
Moreover,
it
is
unclear
if
the
ACL
or
the
PCL
is
loaded
when
anterior
knee
movement
occurs.
1932
-
8/10/2019 Cruciate Ligament Forces Between Short and Long Step Forward Lunge
2/11
The
forward
lunge
can be performed
and progressed
using
varying
techniques. One technique involves
starting in
an
upright position,
stepping
forward
with the lead leg
and
flexing
the
lead knee until
the rear
knee
touches
the ground,
and then pushing
back
to the
starting
upright position. Be -
cause a stride
is
taken by the lead leg
during each repetition,
this
technique may
be called
a
forward
lunge with a stride.
Another
technique
involves
first stepping forward
with the
lead
leg
and starting with both
knees fully extended. From
this
position,
the individual
flexes the lead
knee until
the rear
knee touches
the
ground,
and then
both knees are
extended
back to
the
starting
position.
In this
technique,
which
has
been
previously
described
(16), both feet
remain stationary
as
the
individual lunges
up and down. Because this tech-
nique
does
not involve striding
forward
during each repeti-
tion, this technique
may be
called a
forward
lunge without a
stride. The lunge
with
a
stride can
be a
progression of the
lunge without
a
stride, with the lunge without a
stride being
a
beginning exercise and the
lunge with a stride being more
difficult
to
perform and advanced. The lunge with
a
stride
requires higher levels
of
lower
body strength
and
coordina-
tion
compared
with
the lunge without
a
stride.
Understanding
how
cruciate ligaments are loaded differ-
ently among these technique variations of the forward lunge
may allow clinicians to prescribe safer and more effective
knee rehabilitation treatment to
patients
during ACL
or PC L
rehabilitation. For example, during the forward
lunge,
if
ACL
loading occurs
when
using
a
short
step but not
when
using
a
long
step,
the forward
lunge
with
a long
step
may be
more appropriate for the patient
if
the
clinician's immediate
goal for the
patient
is
to
minimize
ACL
loading. Similarly,
during the forward lunge, if
PCL
loading occurs with a stride
but not without
a
stride, the forward lunge without
a
stride
may be more appropriate for the patient if the clinician's
immediate goal
for
the patient
is
to minimize
PCL
loading.
Our
purpose was
to
compare cruciate ligament tensile
forces
while
performing
the
forward
lunge with a
long step
(forward lunge long), with
a short
step
(forward
lunge short),
with a stride, and without a stride.
It
was
hypothesized
that
ACL tensile
forces
would
be greater
in
the forward
lunge
short compared
with the
forward
lunge long, PCL tensile
forces would
be
greater
in
the forward lunge long compared
with the forward lunge short,
and PCL
tensile forces would
be greater during the forward lunge with a stride compared
with
without a
stride.
Muscle
force
magnitudes in each
subject's
quadriceps and
hamstrings
will also
be
estimated
to
help
better understand ACL
and
PCL
force
magnitudes.
METHO S
Subjects.
Eighteen healthy
individuals (nine men and
nine
women) without
a history of
cruciate ligament pathol-
ogy participated with an average age, mass, and height of
29
t 7 yr, 77
9
kg,
and
177
6 cm, respectively,
for me n
and 25
2
yr,
60
4
kg,
and
164 6 cm, respectively, for
women. All subjects were required to perform the forward
lunge
exercises
pain free
and
with proper
form
and tech-
nique for 12 consecutive
repetitions using
their 12-repetition
maximum (12RM)
weight.
To control the EMG signal quality, this study was limited
to men and women who had average
or below
average
body
fat, which
was
assessed by
the
Baseline skinfold calipers
(Model
68900;
Country Technology,
Inc., Gays Mills, WI),
and appropriate
regression equations
and
body
fat standards
set
by the American
College
of Sports Medicine
(3).
Aver-
age
body
fat
was
12%
4%
for
men and
18%
1
for
women. The protocol used in
the current
study
was approved
by the institutional
review board
at the California
State Uni-
versity,
Sacramento, CA,
and
all
subjects
provided
written
informed
consent.
Exercise
description. Each subject performed
the
for-
ward lunge long
(Fig. 1) and
the
forward
lunge short
(Fig. 2)
with and without a stride. The starting and the ending posi-
tions
of
the forward
lunge long
with stride and forward lunge
short with stride were the same, which involved standing
upright
with
both feet
together and
the
knees
fully
extended
(full
knee extension
= knee
angle). From this
position, the
subject held
a
dumbbell weight
in each
hand
and lunged
forward with the right leg toward
a
force platform
at
ground
level. At right foot
contact, the
right
knee
flexed at
approxi-
mately
45.s-I
until
approximately
9001000
knee angle, at
which time the left knee made contact
with
the
ground. From
this position,
the
subject immediately pushed backward
the force platform
and returned to the upright standing posi-
tion with feet together.
During the forward lunge
long,
each
subject
used
a
long
step
length
that resulted in the
right leg
(tibia)
being
approxi-
mately vertical at the lowest position
of
the
lunge (Fig. 1), thus
maintaining
the knee
over
the
foot.
The
average
step
length
(measured from left toe to
right
heel)
for
the forward lunge
FIGURE 1-Fonvard
lunge
with a
long
step (forward
lunge long).
SHORT-STEP
AND LONG-STEP FORWARD LUNGE
Medicine Science in
Sports Exercisee
1933
-
8/10/2019 Cruciate Ligament Forces Between Short and Long Step Forward Lunge
3/11
11111:10 ,j
FIGURE
2-Forward
lunge
with a
short step forward
lunge
short).
long
was
89
+
4
cm
for
men
and
79 :
cm for
women.
Th e
step length
for
the forward
lunge
short
was
one half
the
dis-
tance of
he step
length
of
the
forward
lunge
long.
The
shorter
step
length
for
the
forward
lunge
short
caused
the
anterior
surface
of
the
knee to
translate
beyond
the
distal
end
of the
toes,
as
shown
in Figure
2.
The
forward
lunge
long
and
short
without
stride
was
performed
the same
as
the forward
lunge
long
and
short
with
stride,
with
the
exception
that
during
the
forward
lunge
long
and
short
without
stride
both
feet
remained
stationary
throughout
each repetition.
That
is,
from
the
lowest position
of
he forward
lunge
long
and
short
shown
in
Figures
1 and 2,
the subject
fully
extended
both
knees
and then
flexed
both
knees
returning
back
to
the
lowest
position
of
the lunge.
For
all
lunge
variations,
a
metronome
was
used
to help
ensure
the right
knee
flexed
and
extended
at
a normal
rate
of
ap-
proximately
45-s-
1.During
the
forward
lunge
long
and
short
with
and
without
a
stride,
maximum
forward
trunk
tilt
(which
occurred
near
maximum
lead
knee
flexion)
was
approxi-
mately
10'-20'
for
all
subjects.
Data collection.
Each
subject
came
in for
a
familiar-
ization
session
1 wk
before
the
testing
session.
The
experi-
mental
protocol was
reviewed, the
subject was
given the
opportunity
to practice
the
lunge
variations,
and
each
subject's
step
length for
the
forward
lunge
long
was
determined.
In
ad-
dition,
each
subject's
12RM
was
determined
while
performing
the
forward
lunge
with
stride
using
a
step
length
halfway
be-
tween
the
forward
lunge
long
and
the
forward
lunge
short.
Subjects
used
their
12RM
weight
for
the
four
lunge
variations
during
data
collection.
The
mean
total
dumbbell
mass
used
was
49:
11
kg
for
men
and
32
8 kg
for
women.
To
collect
EMG
data,
Blue
Sensor
(Ambu
Inc.,
Linthicum,
MD)
disposable
surface
electrodes
(type
M-00-S)
22 mm
wide
and
30 mm long were
positioned in a bipolar configuration
along
the
longitudinal
axis of
each
muscle,
with
a center-
to-center
distance
of
approximately
3
cm between
electrodes.
Before
applying
the
electrodes,
the skin
was
prepared
by
shaving,
abrading,
and
cleaning
with
isopropyl
alcohol
wipes
to reduce
skin
impedance.
Each
subject
had
electrode
pairs
positioned
on the
right
side
using
previously
described
locations
(4)
for
the
following
muscles:
a) rectus
femoris,
b) vastus
lateralis,
c)
vastus
medialis,
d)
medial
hamstrings
(semimembranosus
and
semitendinosus),
e) lateral
hamstrings
(biceps
femoris),
and
f)
gastrocnemius
(middle
portion
be-
tween
medial
and lateral
bellies).
Spherical
markers
(3.8
cm
in diameter)
covered
with
3MTM
reflective
tape were
attached
to adhesives
and
posi-
tioned
over
the
following
bony
landmarks:
a) third
meta-
tarsal head
of
he
right
foot,
b)
medial
and
lateral
malleoli
of
the
right
leg, c) upper
edges
of
the
medial
and
lateral
tibial
plateaus
of
the right
knee,
d) posterosuperior
greater
tro-
chanters
of
he
left
and
right
femurs,
and e)
lateral
acromion
of
the
right
shoulder.
After
the
subject
warmed
up
and
practiced
the exercises
as
needed,
data
collection commenced. A six-camera Peak
Performance
motion
analysis
system
(Vicon-Peak
Perfor-
mance
Technologies,
Inc., Englewood,
CO)
collected
60
Hz
of
video
data.
A force
platform
(Model
OR6-6-2000;
Advanced
Mechanical
Technologies,
Inc.,
Watertown,
MA)
collected
960
Hz
of
force
data,
while
a
Noraxon
EMG
system
(Noraxon
USA,
Inc.,
Scottsdale,
AZ)
collected
960
Hz
of
EMG
data.
The
EMG
amplifier
bandwidth
frequency
was
10-500
Hz
with an
input
impedance
of
20,000
k.M,
and
the
common-mode
rejection
ratio
was
130
dB.
Video,
EMG,
and force
data
were
electronically
synchronized
and collected
simultaneously
as
each subject
performed
one set
of
three
repetitions
using their
12RM
weight
of
the forward
lunge
long
with
stride,
forward
lunge
long
without
stride,
forward
FIGURE 3-Computer optimization
with input from measured
knee
torque
from
inverse
dynamics
and
predicted
knee
torque
from
muscle
model,
where
TK
=
resultant
knee
torque,
FK
=
resultant
knee
force,
I
= moment
of
inertia
about
leg center
of
mass, ax
angular
acceleration
of
leg,
=
mass
of
leg, a
- linear
acceleration
of
leg,
g =
gravitation
constant
9.80
mrs-
2
, Fe,t
= external
force acting
on
foot,
T.
external
torque
acting
on
foot,
FQ
=quadriceps
force,
Fp
= patellar
tendon
force,
Fu
=
hamstrings
force,
and
FG
= gastrocnemius
force.
Note-
to
simplify
the
drawing,
the
equal
and
opposite
forces
and
torques
acting
on
the
distal
leg
and
proximal
ankle
are
absent.
http://www.acsrn-msse.org
1934
Official
Journal
of the
American
College
of Sports
Medicine
-
8/10/2019 Cruciate Ligament Forces Between Short and Long Step Forward Lunge
4/11
FIGURE
4-Forces acting
on
the proximal tibia:
F
11
=
force
from
ham-
strings, FG
= force from gastrocnemius (note: this force does not act
directly on
proximal
tibia), Fpr = force
from
patellar tendon, FACL
force from ACL, FpcL
=
force from PCL, and FTF,= force from femur.
lunge
short with stride,
and
forward lunge short without stride,
assigned in
a
random order. Each subject
rested approximately
2-3 min between
lunge variations. Tape markers were used
to
help
each
subject
identify the
proper
stride length distance
between
their rear
and
lead foot for each
lunge variation.
After completing
all
lunge
variations,
each subject per-
formed
maximum voluntary isometric contractions (MVIC)
to
normalize the EMG
data
collected during each
lunge varia-
tion. The MVIC for the rectus femoris,
the vastus lateralis, and
the vastus medialis
were
collected
in a
seated
position at
90 '
knee
and
hip
flexion with
a
maximum effort knee
extension
(13). The MVIC for the
lateral
and medial hamstrings were
collected in
a seated
position at 900 knee
and
hip
flexion
with
a
maximum effort knee flexion (13), with the ankle main-
tained in
a
neutral
position. MVIC
for
the gastrocnemius
was collected
during a maximum effort standing one leg toe
raise
with
the
ankle
positioned
approximately halfway be-
tween neutral
and full plantarflexion (13). Two 5-s
trials
were
randomly collected for each MVIC, with 1-2 min of rest
given between
trials.
, Data
reduction.
Video
images for each reflective
marke r were tracked and digitized in -three-dime nsional
space
with Peak Performance software (version 5.0), using
the direct linear transformation calibration
method
(34).
An -
kle,
knee,
and hip
joint
centers from the link
segment model
were mathematically determined using the external markers
and appropriate equations
as previously
described
(7,13).
Testing of
the accuracy
of
the
calibration system
resulted
in
reflective markers that could be
located
in three-dimensional
space
within
our
laboratory
with an error less than 7 mm. The
raw position data
were
smoothed
with
a
double-pass
fourth-
order Butterworth low-pass filter
with
a
cutoff frequency
of 6 Flz
(13).
Joint angles, linear
and
angular
velocities,
and
linear and
angular
accelerations
were calculated
in
a
two-
dimensional sagittal
plane
of the
knee
using appropriate ki-
nematic equations
(13).
Raw EMG
signals were full-waved rectified,
smoothed
with
a
10-ms moving
average
window, linear enveloped
(5).
throughout the knee range of motion for each repetition, and
normalization
by expressing the data as
a percentage
of each
subject's
highest corresponding MVIC trial. The highest
EMG
signal
over
a
1-s
time
interval throughout
the 5-s
MVIC
was
determined to calculate
MVIC
trials. Normalized EMG
data
for
the
three
repetitions
(trials) were then averaged at
corresponding knee flexion angles between 0' and 90' and
were used
in
the biomechanical model described
below.
TABLE
1.
Mean
t
SD
cruciate ligament force
(N)
alues between forward lunge
step
length variations
and
between forward lunge
stride
variations.
ACL
forces represent
negative values
and
PCL
forces represent
positive values.
Step Length Varialions Stride Variations
Long Step
Short Step P Value
With Stride
Without
Stride P Value
Knee
angles for descent phase
0.
349
i
202
69 169
-
8/10/2019 Cruciate Ligament Forces Between Short and Long Step Forward Lunge
5/11
~ 800
S
0
E? 400
20 0
0
20
40
60
86
lbo
io
Knee
Flexing
(Descent)
Knee i
Knee Flexion
Angle
(deg)
Forward
Lunge
Long
Without
Stride
---
Forward
Lunge
Short
Without
Stride
FIGURE
5-AMean
(SD)
PCL
tensile
force
during
forward
lunge
long
and
short
without
stride.
Biomechanical
model.
As
previously
described
(13,41),
a
biomechanical
model
of
he
knee
(Figs.
3
and
4)
was
used
to
continuously
estimate
cruciate
ligament
forces
throughout
a
90*
knee
range
of
motion
during
the
knee flexing
(squat
de-
scent)
phase
(0o--90')
and
the
knee
extending
(squat
ascent)
phase
(90o0o--)
of
the
lunge.
Resultant
force
and
torque
equilibrium
equations
were
calculated
using
inverse
dynamics
and
the
biomechanical
knee
model
(13,41).
Anteroposterior
shear
forces
in the
knee
were
calculated
and
adjusted
to lig-
ament
orientations
to
estimate
ACL
or
PCL
forces,
while
moment
arms
of
muscle
forces
and
angles
for
the
line
of
ac-
tion
for
the muscles
and
cruciate
ligaments
were
expressed
as
polynomial
functions
of
knee
angle
(23).
Knee
torques
from
cruciate
and
collateral
ligament
forces
and
bony
contact
were
assumed
to be
negligible,
as were
forces
and
torques
out
of
the sagittal
plane.
Quadriceps,
hamstrings,
and
gastrocnemius
muscle
forces
were
estimated
an
EMG-driven
biomechanical
knee
model,
as
previously
described
(13,41).
Because
the
accuracy
of
estimating
muscle
forces
depends
on accurate
estimations
of
C
E
xtending Ascent)
a
muscle's
physiological
cross-sectional
area
(PCSA),
max-
imum
voluntary
contraction
force per
unit
PCSA,
and EMG-
force
relationship,
resultant
force
and
torque
equilibrium
equations may
not
be satisfied. Therefore, the modified
muscle
force
Fm(
equation
at
each
knee
angle
is
as follows:
F.
=
cik1krtA1orm .)
[EMG
1
MV1C
1
],
where
Ai
is
the
PCSA
of
the
ith muscle,
o-m()
is
the
MVIC
force
per
unit
PCSA
of
the
ith
muscle,
EMG
and
MVICi
are
the EMG
window
averages
of
the
ith
muscle
EMG
during
exercise
and MVIC
trials,
ci
is
a
weight
factor
(values
given
below)
adjusted
in
a computer
optimization
program
to
min-
imize
the
difference
between
the
resultant
torque
from
the
inverse
dynamics
(Tw,)
and
the
resultant
torque
calculation
from
the
biomechanical
model
Tin)
(Fig.
3), k l
represents
each
muscle's force-length
relationship
as
function
of hip
and
knee
flexion
angles
(on
the
basis
of
muscle
length,
fiber
length,
sarcomere
length,
pennation
angle,
and cross-sectional
area)
(36),
and
kv
represents
each
muscle's
force-velocity
relationship
on
the
basis
of
a Hill-type
model
for
eccentric
1000-
600
800
400
200
0
-200.
200
2'0 40
60
80
100
8'0
6'0
4 0
20
Knee
Flexing
(Descent)
Knee Extending
(Ascent)
Knee
Flexion
Angle
(deg)
Forward
Lunge
long
Nwith
Stride
-F--
Forward
Lunge
short with
Stride
FIGURE
6-Mean
(SD)
ACL
and
PCL
tensile
force
between
forward
lunge
long
and
short
with
stride.
http://www.acsm-msse.org
1936 Official
Journal
of
the
American
College
of Sports
Medicine
-
8/10/2019 Cruciate Ligament Forces Between Short and Long Step Forward Lunge
6/11
U
0i
Knee Flexing (Descent)
Knee
Extending
(Ascent)
Knee Flexion
Angle (deg)
- Forward
Lunge
Long
with Stride
-
Forward Lunge
Long
without Stride
FIGURE
7-Mean (SD)
PCL
tensile force
during
forward lunge long with
and without
stride.
and concentric
muscle
actions using
the following equations
from Zajac
(40)
and
Epstein
and
Herzog (12):
v =
b
- (a/Fo) ,)/(b
+ v)
concentric
k,. =
C- C- l) b+ a/Fo)v)/ b-
v) eccentric
with Fo representing
isometric
muscle force; lo, muscle
fiber
length at rest;
v, velocity;
a =
0.32
Fr
;
b = 3.210
per second;
and
C
=
1.8.
Ratios
of
PCSA
between muscle
groups (41)
were deter-
mined from the
PCSA data from
Wickiewicz
et al. (36).
According to Narici et
al. (29), the total PCSA
of the quad-
riceps
was
approximately
160 cm
2
for
a
75-kg man, and
the
total PCSA
of the quadriceps
was scaled up or
down by in-
dividual
body
mass
(41). Forces generated
by
the
knee flexors
and extensors at
MVIC
were assumed to
be
linearly pro-
portional to their
PCSA (41).
Muscle force per unit
PCSA
was
35
N.cm-
2
for
the hamstrings
and
gastrocnemius
and
40 N-cm-
2
for the quadriceps
(11,28,29,37).
The
objective function used
to determine each ith
mus-
cle's
coefficient
c,
was as follows:
-in
f
ci)
=
_ I
c 2
+X T.,
T.X
J=t
I-1
subject
to clow
-
8/10/2019 Cruciate Ligament Forces Between Short and Long Step Forward Lunge
7/11
TABLE
2. Mean
+
SD
quadriceps
and
hamstrings
force
values
during forward
lunge exercises.
Quadriceps
(N)
Hamstrings
(N)
Step
Length
Variations
Stride Variations
Step
Length
Variations
Stride
Variations
Long
Step
Short
Step
With
Stride
Without
Stride
Long
Step
Short
Step
With
Stride
Without
Stride
Knee
angles
for descent
phase
0. 87:
84
63
49
80 *
84 71
+ 49
47
121
29 15
22
15 54:20
10* 111
*
67
99:
76
116
89
94
t 55
64
38
28
18
34
30
57*
26
2
131
68
109:
74
135
90
105
t
51
66:
40
31
0
38
34
58:
26
300
179
80
126:
76
158 81
147
75
69 i
39
34
0
46
4
56
25
40*
227
117
157:
94
176
105
207 +
106
67:
39
38;
23
50
7
56 *
25
5
326
163
235
131
258
47
303 146
70:
36
41
27
58
8
53:
25
60*
435
86
344
187
354:
191
425
182
71
41 39 24 63 2 47
23
700
551
204
469
i
247
471 221
549
230
67 43
34
* 21
61
43
41
+ 23
o0o
560
157
527:
239
510
12
577
t
183
60
37
32t
2
51
4
41
:t
23
900
540:
172
599
219
563
196
577
195
57
33
36:
21
49
8
44* 26
Knee
angles
for
ascent
phase
90B
400
120
542
129
459
130
483:
120
1 1
48
99 51
102 49
98:
50
80
434
156
623
211
515
:L
08
542:
159
108
48
94
59
103
58
99
49
7
516
175
681
272
613
264
585 182
120
58
92
2
112
5
1 1
45
600
532
192
658 290
620
283
570:
199
128
3
90:
50
118
70
100
43
50
486:
188
577 278
571
73
492
193
134 64
87
49
122
71
99:
41
400
409
65
437t203
468
212
377
56
139:
71
82
45
122
5
100
41
300
336
i 144
349:
165
410
191
275:
118
143 4
84
42
125
75
102
1
2
268
19
257
24
338:
166
187
7
140
75
83 +
42
120
76
103
2
10*
206
05
183
1 1
269
49
119
57
142
80
81 41
119 81
104
0
0. 136 0 141
0 199
127
79 3,
121
t 84
70
6 88
4 103
36
variations
and
stride
variations)
repeated-measures
ANOVA.
To minimize
the
probability
of
type I
errors
secondary
to
the
use of
a
separate
ANOVA
for
each
knee
angle,
the
Bonferroni
adjustment
had
a
level of
significance
set
at P