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Journal of Biomechanics 32 (1999) 13—17
Intra-abdominal pressure mechanism for stabilizing the lumbar spine
Jacek Cholewicki *, Krishna Juluru , Stuart M. McGill
Biomechanics Research Laboratory, Department of Orthopaedics and Rehabilitation, Yale University School of Medicine, P.O. Box 208071, New Haven,
CT 06510, U.S.A.
Occupational Biomechanics Laboratories, Department of Kinesiology, Faculty of Applied Health Sciences, University of Waterloo, Waterloo,
Ont., Canada N2L 3G1
Received in final form 3 February 1998
Abstract
Currently, intra-abdominal pressure (IAP) is thought to provide stability to the lumbar spine, but the exact principles have yet to be
specified. A simplified physical model was constructed and theoretical calculations performed to illustrate a possible intra-abdominal
pressure mechanism for stabilizing the spine. The model consisted of an inverted pendulum with linear springs representing
abdominal and erector spinae muscle groups. The IAP force was simulated with a pneumatic piston activated with compressed air.
The critical load of the model was calculated theoretically based on the minimum potential energy principle and obtained
experimentally by increasing weight on the model until the point of buckling. Two distinct mechanisms were simulated separately and
in combination. One was antagonistic flexor—extensor muscle coactivation and the second was abdominal muscle activation along
with generation of IAP. Both mechanisms were effective in stabilizing the model of a lumbar spine. The critical load and therefore the
stability of the spine model increased with either increased antagonistic muscle coactivation forces or increased IAP along with
increased abdominal spring force. Both mechanisms were also effective in providing mechanical stability to the spine model when
activated simultaneously. Theoretical calculation of the critical load agreed very well with experimental results (9.5% average error).
The IAP mechanism for stabilizing the lumbar spine appears preferable in tasks that demand trunk extensor moment such as lifting or
jumping. This mechanism can increase spine stability without the additional coactivation of erector spinae muscles. 1999 Elsevier
Science Ltd. All rights reserved.
Keywords: Intra-abdominal pressure; Lumbar spine; Stability
1. Introduction
An increase in the intra-abdominal pressure (IAP) is
commonly observed when a large load is placed on the
spine during everyday activities like running, jumping,
and lifting (e.g. David, 1985; Davis, 1959; Davis and
Troup, 1964; Hemborg et al., 1983; Marras and Mirka,
1996; Mairiaux et al., 1984; Troup et al., 1983). The
function of this increase in pressure is still not well
understood. Early hypotheses stated that pressure within
the abdominal cavity may provide some load relief to the
lumbar spine (Bartelink, 1959; Keith, 1923; Morris et al.,
1961). Formulation of these hypotheses was based on the
concept that pressure, produced within the abdominal
cavity exerted a hydrostatic force down on the pelvic
* Corresponding author. Tel.: 203 737 2887; fax: 203 785 7069; e-mail:
cholewicki@biomed.med.yale.edu
floor and up on the diaphragm. This force added tension
to the spine, produced trunk extension moment and,
therefore, was assumed to reduce spine compression
force. However, the many studies that followed failed to
provide any evidence to support the original IAP hy-
pothesis (Bearn, 1961; Krag et al., 1984, 1985, 1986;
McGill and Norman, 1987; Nachemson et al., 1986;
Ortengreen et al., 1981). A forceful contraction of abdom-
inal muscles is necessary to generate IAP. It seems that
the spine compressive forces, arising from such contrac-
tion, offset the beneficial action of the hydrostatic forces
thought to alleviate spinal compression via IAP.
The currently prevailing hypothesis appears to be that
IAP provides stability to the lumbar spine (Cresswell
et al., 1994; Marras and Mirka, 1996; McGill and Nor-
man, 1987; McGill and Sharratt, 1990; Tesh et al., 1987).
Mechanical stability of the lumbar spine must be main-
tained at all times to prevent its buckling and subsequent
injuries when the spine is loaded during physical activities
0021-9290/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 2 1 - 9 2 9 0 ( 9 8 ) 0 0 1 2 9 - 8
(Cholewicki and McGill, 1996). The abdominal wall
muscles, contracting against the pressurized peritoneal
cavity, may stabilize the spine and trunk. However, the
exact principles have yet to be described.
The purpose of the present study was to formulate an
analytical model to illustrate a possible intra-abdominal
pressure mechanism for stabilizing the lumbar spine. In
addition, the experiments with a physical model were
conducted to verify the proposed theoretical concepts.
The question asked was whether it is possible to stabilize
the lumbar spine by increasing intra-abdominal pressure.
2. Theory
It is well established that skeletal muscle stiffness is
proportional to the muscle force (see literature review in
Cholewicki and McGill, 1995). Therefore, contracting
muscles that surround the lumbar spine can increase its
stiffness and stability (Cholewicki and McGill, 1996;
Cholewicki et al., 1997; Gardner-Morse et al., 1995). This
increase in spine stability can, theoretically, be accomp-
lished by two mechanisms: antagonistic muscle coactiva-
tion (Gardner-Morse and Stokes, 1998) and/or an
increase in intra-abdominal pressure (IAP). The latter
hypothesized mechanism is based on the premise that the
increase in the IAP is accomplished by the contraction of
the abdominal musculature (Cresswell and Thorsten-
sson, 1989; Cresswell et al., 1994; Grillner et al., 1978;
Fig. 1. Anatomical diagram (A) of the lumbar spine, ribcage, pelvis,
abdominal and erector spinae musculature, and intra-abdominal pres-
sure represented in the physical model (B). The pivot corresponded to
an L5-S1 intervertebral joint. Linear springs represented abdominal
and erector spinae muscles and a pneumatic piston placed halfway
between the pivot and abdominal spring attachment point simulated
the intra-abdominal pressure. All the dimensions are expressed in
millimeters.
McGill and Sharratt, 1990). Because the compressive
force of the contracting abdominal wall muscles cancels
out the hydrostatic IAP force acting on the spine, the
IAP results in non-significant net forces or moments.
However, the contracted abdomen constitutes a much
stiffer structure that will increase the overall stability of
the lumbar spine (Fig. 1A). An important feature of such
a mechanism is the ability to increase spine stability
without the penalty of additional erector spinae muscle
co-activation.
3. Methods
To assess the feasibility of the proposed theory for
increasing the lumbar spine stability with an intra-ab-
dominal pressure mechanism, a simplified physical
model was constructed and tested (Fig. 1B). The model
consisted of an inverted pendulum with a pivot repres-
enting the L5-S1 intervertebral joint. The 20 cm height of
the pendulum shaft corresponded to an average distance
between the L5 and T9. The T9 vertebra was the level at
which the approximate location of the center of trunk
mass was assumed. Linear springs spanning the pivot
represented abdominal and erector spinae muscles with
moment arms of 8.5 and 6.0 cm, respectively. A hydros-
tatic force generated by the IAP was simulated with
a pneumatic piston placed halfway between the pivot and
abdominal spring attachment point. The piston had a 16-
mm diameter and was activated with a compressed air
introduced from a cylinder through a pressure regulator.
Critical load (load at which the inverted pendulum just
begins to buckle) of the model in a vertical equilibrium
Fig. 2. Two spine-stabilizing mechanisms: The coactivation of the ab-
dominal and erector spinae muscles (CC), the intra-abdominal mecha-
nism (IAP), and both mechanisms combined (CC#IAP).
14 J. Cholewicki et al. / Journal of Biomechanics 32 (1999) 13—17
Table 1
Intra-abdominal pressure and muscle coactivation patterns simulated in this study. CC-coactivation, IAP-intra-abdominal pressure mechanism (refer
to Fig. 2)
Mechanism Total spring stiffness on Total spring stiffness on Cylinder pressure Experimental Theoretical
the abdominal side the erector spinae side (kPa) P
!0
(N) P
!0
(N)
(N/m) (N/m)
CC 1 414.0 1015.5 0 35.22 33.23
CC 2 1054.9 2110.1 0 89.24 76.09
CC 3 2402.8 3483.4 0 141.45 149.50
IAP 1 1054.9 0 310 42.96 38.12
IAP 2 2070.4 0 530 90.05 74.79
IAP 3 3443.7 0 800 137.54 124.40
CC#IAP 3443.7 2997.9 550 171.87 178.37
position was determined for various muscle and/or IAP
activation schemes experimentally (by placing dead
weight) and analytically with a theoretical model (see the
appendix).
Two distinct spine-stabilizing mechanisms were
simulated. First, the coactivation of the abdominal and
erector spinae muscles was accomplished by attaching
representative springs and adjusting their pre-tension to
achieve equilibrium (Fig. 2 CC). Adding springs in paral-
lel or replacing them with springs of higher stiffness
simulated the increase in muscle coactivation. In this
way, increased muscle force and stiffness was accomp-
lished simultaneously. No IAP was activated in this case.
Second, equilibrating pressure in the cylinder against the
abdominal spring force simulated the IAP mechanism
(Fig. 2 IAP). Higher IAP levels were achieved by increas-
ing pressure in the cylinder and adding more springs in
parallel on the abdominal muscles’ side. The erector
spinae springs were completely disconnected. Three
levels of muscle coactivation and three levels of IAP were
tested. Finally, one case of both mechanisms combined
was simulated (Fig. 2 CC#IAP). All of the above cases
are listed in Table 1.
4. Results
Both mechanisms simulated in this study, the muscle
coactivation and intra-abdominal pressure (IAP), were
effective in stabilizing the model of a lumbar spine
(Fig. 3). The critical load and, therefore, the stability of
the spine model increased with either increased muscle
coactivation forces (added springs in parallel) or in-
creased IAP along with increased abdominal spring
force. Both mechanisms were also effective in pro-
viding the mechanical stability to the spine model when
activated simultaneously (Fig. 3). Theoretical cal-
culation of the critical load agreed very well with exp-
erimental results (Fig. 3). Average error was 9.5%
(S.D.5.0%).
Fig. 3. Critical loads determined theoretically and experimentally us-
ing a physical model for various muscle activation patterns simulated in
this study. The critical load and, therefore, the stability of the spine
model increased with simulation of either increased antagonistic muscle
coactivation, increased IAP along with increased abdominal muscle
force, or both mechanisms combined. CC-coactivation, IAP-intra-ab-
dominal pressure mechanism (refer to Table 1).
5. Discussion
An analytical model, illustrating a possible intra-ab-
dominal pressure (IAP) mechanism for stabilizing the
lumbar spine, was presented in this study. Validity of the
theoretical model was verified by determining the critical
load experimentally in a physical model. Calculated
values of the critical load agreed very well, but were
slightly lower than the critical load obtained experi-
mentally. Most likely the friction in the physical model’s
joint provided some resistance to small perturbations in
the experiment. This friction was not accounted for in the
theoretical calculations.
This is a very simple one degree-of-freedom model that
cannot fully reflect the complexity of stability issues in a
J. Cholewicki et al. / Journal of Biomechanics 32 (1999) 13—17 15
human lumbar spine system. No attempt was made to
simulate the cross-sectional area of the diaphragm with
the pneumatic piston or the realistic muscle forces with
springs. This model was not intended for future calcu-
lations and simulations. Future modeling studies should
incorporate three-dimensional and multi-joint features
and other anatomical details. Rather, the utility of this
model was to illustrate principles that will most likely
hold true in a real multi degree-of-freedom spine system.
One such principle may be that the IAP itself does not
stabilize the spine. Rather, it is the stiffness of the abdom-
inal muscles generating the IAP that increases spine
stability. In other words, activation levels of all trunk
muscles determine the stability of the spine, regardless of
the magnitude of generated IAP.
The IAP mechanism for stabilizing the lumbar spine
presented here is consistent with several in vivo studies
reported in the literature. Krag et al. (1994, 1995, and
1996) found no difference in erector spinae muscle activ-
ity during lifting tasks when various levels of IAP were
utilized. If the IAP indeed serves to stabilize the lumbar
spine, these results support the mechanism outlined in
the current study, by which no change in erector spinae
muscles is necessary. Marras and Mirka (1996) sought
the relationship between the IAP and various trunk
extension motions. Although some patterns were seen,
the IAP correlated more consistently with the activity of
external oblique muscles. Based on their findings, the
authors concluded that IAP might simply be a by-prod-
uct of trunk muscle activation and coactivation.
Two distinct mechanisms for stabilizing the lumbar
spine were simulated in this study. One involved the
well-accepted notion of antagonistic muscle coactivation
around a given joint (Cholewicki et al., 1997; Gardner-
Morse and Stokes, 1998). However, trunk flexor—exten-
sor muscle coactivation requires a certain portion of the
extensor muscle resources to be dedicated to equilibrat-
ing the abdominal muscle contraction. The second mech-
anism, illustrated here, was via generation of IAP. The
IAP mechanism for stabilizing the lumbar spine appears
to be preferable especially during tasks that demand
trunk extensor moment such as lifting or jumping. This
mechanism can increase spine stability without the addi-
tional coactivation of erector spinae muscles. Only the
abdominal muscles are contracted against the hydros-
tatic pressure in an abdominal cavity. Full capacity of
trunk extensors is therefore available for executing the
tasks. Notwithstanding this advantage, it is likely that
a combination of both spine-stabilizing mechanisms, in
varying proportions, is utilized by the neuromuscular
system in vivo. Indeed, Cholewicki et al. (1998) found
that increased trunk stiffness resulting from the Valsalva
maneuver was associated with significantly higher activity
of abdominal and erector spinae muscles. The question
of whether both mechanisms (antagonist co-activation
and IAP with abdominal activation) can occur separately
or in combination remains to be answered by in vivo
experimentation.
Inappropriate coordination of trunk muscle recruit-
ment patterns to stabilize the lumbar spine through an-
tagonistic coactivation and IAP may predispose an indi-
vidual to sustain a low back injury during a physical
activity. Cholewicki and McGill (1996) and McGill
(1997) proposed an explanation for low back injury based
on mechanical stability principles. Simply, buckling of
a spine is possible, if it is not stiffened adequately. These
studies suggest that muscle contraction together with
elevated IAP can effectively stiffen the spine to achieve
sufficient stability level. Future studies should be de-
signed to directly test the proposed IAP mechanism
for stabilizing lumbar spine and to define magnitudes
of muscle coactivation and IAP necessary to prevent
buckling.
Acknowledgements
Financial support for this study was provided by the
Gaylord Rehabilitation Research Institute grant.
Appendix
Calculations of the critical load (P
!0
) were based on
the minimum potential energy principle, which states
that for a system to be in a stable equilibrium, its poten-
tial energy must be at a relative minimum. In other
words, the second derivative of the model’s potential
energy with respect to small deflection angle must be
greater than zero. The potential energy (») was taken to
be the elastic energy stored in the abdominal (» ) and
erector spinae (» ) springs minus the work done by the
external load (¼
) and by the pressurized cylinder (¼ ):
»( )» ( )#» ( )!¼
J
( )!¼ ( ), (A.1)
where is the deflection angle of the pendulum from
vertical. The elastic energy stored in the abdominal
spring is
» ( )F x #

k x, (A.2)
where F is an initial force in the spring, k is spring
stiffness, and x is length change of the spring upon
a small deflection ( ) of the pendulum. The elastic energy
stored in the erector spinae spring was calculated using
the same equation replacing subscripts ‘a’ with ‘e’. The
work performed by the external load is
¼

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Plugin jacek%20-%20 intra-abdominal%20pressure%20mechanism%20for%20stabilizing%20the%20lumbar%20spine

  • 1. Journal of Biomechanics 32 (1999) 13—17 Intra-abdominal pressure mechanism for stabilizing the lumbar spine Jacek Cholewicki *, Krishna Juluru , Stuart M. McGill Biomechanics Research Laboratory, Department of Orthopaedics and Rehabilitation, Yale University School of Medicine, P.O. Box 208071, New Haven, CT 06510, U.S.A. Occupational Biomechanics Laboratories, Department of Kinesiology, Faculty of Applied Health Sciences, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 Received in final form 3 February 1998 Abstract Currently, intra-abdominal pressure (IAP) is thought to provide stability to the lumbar spine, but the exact principles have yet to be specified. A simplified physical model was constructed and theoretical calculations performed to illustrate a possible intra-abdominal pressure mechanism for stabilizing the spine. The model consisted of an inverted pendulum with linear springs representing abdominal and erector spinae muscle groups. The IAP force was simulated with a pneumatic piston activated with compressed air. The critical load of the model was calculated theoretically based on the minimum potential energy principle and obtained experimentally by increasing weight on the model until the point of buckling. Two distinct mechanisms were simulated separately and in combination. One was antagonistic flexor—extensor muscle coactivation and the second was abdominal muscle activation along with generation of IAP. Both mechanisms were effective in stabilizing the model of a lumbar spine. The critical load and therefore the stability of the spine model increased with either increased antagonistic muscle coactivation forces or increased IAP along with increased abdominal spring force. Both mechanisms were also effective in providing mechanical stability to the spine model when activated simultaneously. Theoretical calculation of the critical load agreed very well with experimental results (9.5% average error). The IAP mechanism for stabilizing the lumbar spine appears preferable in tasks that demand trunk extensor moment such as lifting or jumping. This mechanism can increase spine stability without the additional coactivation of erector spinae muscles. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Intra-abdominal pressure; Lumbar spine; Stability 1. Introduction An increase in the intra-abdominal pressure (IAP) is commonly observed when a large load is placed on the spine during everyday activities like running, jumping, and lifting (e.g. David, 1985; Davis, 1959; Davis and Troup, 1964; Hemborg et al., 1983; Marras and Mirka, 1996; Mairiaux et al., 1984; Troup et al., 1983). The function of this increase in pressure is still not well understood. Early hypotheses stated that pressure within the abdominal cavity may provide some load relief to the lumbar spine (Bartelink, 1959; Keith, 1923; Morris et al., 1961). Formulation of these hypotheses was based on the concept that pressure, produced within the abdominal cavity exerted a hydrostatic force down on the pelvic * Corresponding author. Tel.: 203 737 2887; fax: 203 785 7069; e-mail: cholewicki@biomed.med.yale.edu floor and up on the diaphragm. This force added tension to the spine, produced trunk extension moment and, therefore, was assumed to reduce spine compression force. However, the many studies that followed failed to provide any evidence to support the original IAP hy- pothesis (Bearn, 1961; Krag et al., 1984, 1985, 1986; McGill and Norman, 1987; Nachemson et al., 1986; Ortengreen et al., 1981). A forceful contraction of abdom- inal muscles is necessary to generate IAP. It seems that the spine compressive forces, arising from such contrac- tion, offset the beneficial action of the hydrostatic forces thought to alleviate spinal compression via IAP. The currently prevailing hypothesis appears to be that IAP provides stability to the lumbar spine (Cresswell et al., 1994; Marras and Mirka, 1996; McGill and Nor- man, 1987; McGill and Sharratt, 1990; Tesh et al., 1987). Mechanical stability of the lumbar spine must be main- tained at all times to prevent its buckling and subsequent injuries when the spine is loaded during physical activities 0021-9290/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 8 ) 0 0 1 2 9 - 8
  • 2. (Cholewicki and McGill, 1996). The abdominal wall muscles, contracting against the pressurized peritoneal cavity, may stabilize the spine and trunk. However, the exact principles have yet to be described. The purpose of the present study was to formulate an analytical model to illustrate a possible intra-abdominal pressure mechanism for stabilizing the lumbar spine. In addition, the experiments with a physical model were conducted to verify the proposed theoretical concepts. The question asked was whether it is possible to stabilize the lumbar spine by increasing intra-abdominal pressure. 2. Theory It is well established that skeletal muscle stiffness is proportional to the muscle force (see literature review in Cholewicki and McGill, 1995). Therefore, contracting muscles that surround the lumbar spine can increase its stiffness and stability (Cholewicki and McGill, 1996; Cholewicki et al., 1997; Gardner-Morse et al., 1995). This increase in spine stability can, theoretically, be accomp- lished by two mechanisms: antagonistic muscle coactiva- tion (Gardner-Morse and Stokes, 1998) and/or an increase in intra-abdominal pressure (IAP). The latter hypothesized mechanism is based on the premise that the increase in the IAP is accomplished by the contraction of the abdominal musculature (Cresswell and Thorsten- sson, 1989; Cresswell et al., 1994; Grillner et al., 1978; Fig. 1. Anatomical diagram (A) of the lumbar spine, ribcage, pelvis, abdominal and erector spinae musculature, and intra-abdominal pres- sure represented in the physical model (B). The pivot corresponded to an L5-S1 intervertebral joint. Linear springs represented abdominal and erector spinae muscles and a pneumatic piston placed halfway between the pivot and abdominal spring attachment point simulated the intra-abdominal pressure. All the dimensions are expressed in millimeters. McGill and Sharratt, 1990). Because the compressive force of the contracting abdominal wall muscles cancels out the hydrostatic IAP force acting on the spine, the IAP results in non-significant net forces or moments. However, the contracted abdomen constitutes a much stiffer structure that will increase the overall stability of the lumbar spine (Fig. 1A). An important feature of such a mechanism is the ability to increase spine stability without the penalty of additional erector spinae muscle co-activation. 3. Methods To assess the feasibility of the proposed theory for increasing the lumbar spine stability with an intra-ab- dominal pressure mechanism, a simplified physical model was constructed and tested (Fig. 1B). The model consisted of an inverted pendulum with a pivot repres- enting the L5-S1 intervertebral joint. The 20 cm height of the pendulum shaft corresponded to an average distance between the L5 and T9. The T9 vertebra was the level at which the approximate location of the center of trunk mass was assumed. Linear springs spanning the pivot represented abdominal and erector spinae muscles with moment arms of 8.5 and 6.0 cm, respectively. A hydros- tatic force generated by the IAP was simulated with a pneumatic piston placed halfway between the pivot and abdominal spring attachment point. The piston had a 16- mm diameter and was activated with a compressed air introduced from a cylinder through a pressure regulator. Critical load (load at which the inverted pendulum just begins to buckle) of the model in a vertical equilibrium Fig. 2. Two spine-stabilizing mechanisms: The coactivation of the ab- dominal and erector spinae muscles (CC), the intra-abdominal mecha- nism (IAP), and both mechanisms combined (CC#IAP). 14 J. Cholewicki et al. / Journal of Biomechanics 32 (1999) 13—17
  • 3. Table 1 Intra-abdominal pressure and muscle coactivation patterns simulated in this study. CC-coactivation, IAP-intra-abdominal pressure mechanism (refer to Fig. 2) Mechanism Total spring stiffness on Total spring stiffness on Cylinder pressure Experimental Theoretical the abdominal side the erector spinae side (kPa) P !0 (N) P !0 (N) (N/m) (N/m) CC 1 414.0 1015.5 0 35.22 33.23 CC 2 1054.9 2110.1 0 89.24 76.09 CC 3 2402.8 3483.4 0 141.45 149.50 IAP 1 1054.9 0 310 42.96 38.12 IAP 2 2070.4 0 530 90.05 74.79 IAP 3 3443.7 0 800 137.54 124.40 CC#IAP 3443.7 2997.9 550 171.87 178.37 position was determined for various muscle and/or IAP activation schemes experimentally (by placing dead weight) and analytically with a theoretical model (see the appendix). Two distinct spine-stabilizing mechanisms were simulated. First, the coactivation of the abdominal and erector spinae muscles was accomplished by attaching representative springs and adjusting their pre-tension to achieve equilibrium (Fig. 2 CC). Adding springs in paral- lel or replacing them with springs of higher stiffness simulated the increase in muscle coactivation. In this way, increased muscle force and stiffness was accomp- lished simultaneously. No IAP was activated in this case. Second, equilibrating pressure in the cylinder against the abdominal spring force simulated the IAP mechanism (Fig. 2 IAP). Higher IAP levels were achieved by increas- ing pressure in the cylinder and adding more springs in parallel on the abdominal muscles’ side. The erector spinae springs were completely disconnected. Three levels of muscle coactivation and three levels of IAP were tested. Finally, one case of both mechanisms combined was simulated (Fig. 2 CC#IAP). All of the above cases are listed in Table 1. 4. Results Both mechanisms simulated in this study, the muscle coactivation and intra-abdominal pressure (IAP), were effective in stabilizing the model of a lumbar spine (Fig. 3). The critical load and, therefore, the stability of the spine model increased with either increased muscle coactivation forces (added springs in parallel) or in- creased IAP along with increased abdominal spring force. Both mechanisms were also effective in pro- viding the mechanical stability to the spine model when activated simultaneously (Fig. 3). Theoretical cal- culation of the critical load agreed very well with exp- erimental results (Fig. 3). Average error was 9.5% (S.D.5.0%). Fig. 3. Critical loads determined theoretically and experimentally us- ing a physical model for various muscle activation patterns simulated in this study. The critical load and, therefore, the stability of the spine model increased with simulation of either increased antagonistic muscle coactivation, increased IAP along with increased abdominal muscle force, or both mechanisms combined. CC-coactivation, IAP-intra-ab- dominal pressure mechanism (refer to Table 1). 5. Discussion An analytical model, illustrating a possible intra-ab- dominal pressure (IAP) mechanism for stabilizing the lumbar spine, was presented in this study. Validity of the theoretical model was verified by determining the critical load experimentally in a physical model. Calculated values of the critical load agreed very well, but were slightly lower than the critical load obtained experi- mentally. Most likely the friction in the physical model’s joint provided some resistance to small perturbations in the experiment. This friction was not accounted for in the theoretical calculations. This is a very simple one degree-of-freedom model that cannot fully reflect the complexity of stability issues in a J. Cholewicki et al. / Journal of Biomechanics 32 (1999) 13—17 15
  • 4. human lumbar spine system. No attempt was made to simulate the cross-sectional area of the diaphragm with the pneumatic piston or the realistic muscle forces with springs. This model was not intended for future calcu- lations and simulations. Future modeling studies should incorporate three-dimensional and multi-joint features and other anatomical details. Rather, the utility of this model was to illustrate principles that will most likely hold true in a real multi degree-of-freedom spine system. One such principle may be that the IAP itself does not stabilize the spine. Rather, it is the stiffness of the abdom- inal muscles generating the IAP that increases spine stability. In other words, activation levels of all trunk muscles determine the stability of the spine, regardless of the magnitude of generated IAP. The IAP mechanism for stabilizing the lumbar spine presented here is consistent with several in vivo studies reported in the literature. Krag et al. (1994, 1995, and 1996) found no difference in erector spinae muscle activ- ity during lifting tasks when various levels of IAP were utilized. If the IAP indeed serves to stabilize the lumbar spine, these results support the mechanism outlined in the current study, by which no change in erector spinae muscles is necessary. Marras and Mirka (1996) sought the relationship between the IAP and various trunk extension motions. Although some patterns were seen, the IAP correlated more consistently with the activity of external oblique muscles. Based on their findings, the authors concluded that IAP might simply be a by-prod- uct of trunk muscle activation and coactivation. Two distinct mechanisms for stabilizing the lumbar spine were simulated in this study. One involved the well-accepted notion of antagonistic muscle coactivation around a given joint (Cholewicki et al., 1997; Gardner- Morse and Stokes, 1998). However, trunk flexor—exten- sor muscle coactivation requires a certain portion of the extensor muscle resources to be dedicated to equilibrat- ing the abdominal muscle contraction. The second mech- anism, illustrated here, was via generation of IAP. The IAP mechanism for stabilizing the lumbar spine appears to be preferable especially during tasks that demand trunk extensor moment such as lifting or jumping. This mechanism can increase spine stability without the addi- tional coactivation of erector spinae muscles. Only the abdominal muscles are contracted against the hydros- tatic pressure in an abdominal cavity. Full capacity of trunk extensors is therefore available for executing the tasks. Notwithstanding this advantage, it is likely that a combination of both spine-stabilizing mechanisms, in varying proportions, is utilized by the neuromuscular system in vivo. Indeed, Cholewicki et al. (1998) found that increased trunk stiffness resulting from the Valsalva maneuver was associated with significantly higher activity of abdominal and erector spinae muscles. The question of whether both mechanisms (antagonist co-activation and IAP with abdominal activation) can occur separately or in combination remains to be answered by in vivo experimentation. Inappropriate coordination of trunk muscle recruit- ment patterns to stabilize the lumbar spine through an- tagonistic coactivation and IAP may predispose an indi- vidual to sustain a low back injury during a physical activity. Cholewicki and McGill (1996) and McGill (1997) proposed an explanation for low back injury based on mechanical stability principles. Simply, buckling of a spine is possible, if it is not stiffened adequately. These studies suggest that muscle contraction together with elevated IAP can effectively stiffen the spine to achieve sufficient stability level. Future studies should be de- signed to directly test the proposed IAP mechanism for stabilizing lumbar spine and to define magnitudes of muscle coactivation and IAP necessary to prevent buckling. Acknowledgements Financial support for this study was provided by the Gaylord Rehabilitation Research Institute grant. Appendix Calculations of the critical load (P !0 ) were based on the minimum potential energy principle, which states that for a system to be in a stable equilibrium, its poten- tial energy must be at a relative minimum. In other words, the second derivative of the model’s potential energy with respect to small deflection angle must be greater than zero. The potential energy (») was taken to be the elastic energy stored in the abdominal (» ) and erector spinae (» ) springs minus the work done by the external load (¼
  • 5. ) and by the pressurized cylinder (¼ ): »( )» ( )#» ( )!¼ J ( )!¼ ( ), (A.1) where is the deflection angle of the pendulum from vertical. The elastic energy stored in the abdominal spring is » ( )F x # k x, (A.2) where F is an initial force in the spring, k is spring stiffness, and x is length change of the spring upon a small deflection ( ) of the pendulum. The elastic energy stored in the erector spinae spring was calculated using the same equation replacing subscripts ‘a’ with ‘e’. The work performed by the external load is ¼
  • 6. P h
  • 7. , (A.3) where P is the external force and h
  • 8. is the height change upon a small deflection ( ) of the pendulum. The work performed by the cylinder force was calculated using the same equation. Substituting Eqs. (A.3) and (A.2) with 16 J. Cholewicki et al. / Journal of Biomechanics 32 (1999) 13—17
  • 9. appropriate geometrical relationships into (A.1) yielded a nonlinear expression for potential energy of the model. This expression was linearized with Taylor series expan- sion to second order and twice differentiated with respect to ( ). The resulting expression was set equal to zero and solved for the critical external load (P !0 ): P !0 k s#k s ¸ (A.4) where s and s are moment arms of abdominal and erector spinae springs and ¸ is the pendulum height as well as the initial length of the springs. References Bartelink, D.L., 1957. The role of abdominal pressure in relieving the pressure on the lumbar intervertebra discs. Journal of Bone and Joint Surgery 39B, 718—725. Bearn, J.G., 1961. The significance of the activity of the abdominal muscles in weight lifting. Acta Anatomica 45, 83—89. Cholewicki, J., McGill, S.M., 1995. Relationship between muscle force and stiffness in the whole mammalian muscle: A simulation study. ASME Journal of Biomechanical Engineering 117, 339—342. 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Nachemson, A.L., Andersson, G.B.J., Schultz, A.B., 1986. Valsalva manoeuvre biomechanics: effects on lumbar trunk loads of elevated intra-abdominal pressures. Spine 11, 476—479. Ortengren, R., Andersson, G.B.J., Nachemson, A.L., 1981. Studies of relationships between lumbar disc pressure, mayoelectric back muscle activity and intra-abdominal (intragastric) pressure. Spine 6, 76—82. Tesh, K.M., Dunn, J.S., Evans, J.H., 1987. The abdominal muscles and vertebral stability. Spine 12, 501—508. Troup, J.D.G., Leskinen, T.P.J., Sta lhammar, H.R., Kuorinka, I.A.A., 1983. A comparison of intraabdominal pressure increases, hip torque, and lumbar vertebral compression in different lifting techniques. Human Factors 25, 517—525. J. Cholewicki et al. / Journal of Biomechanics 32 (1999) 13—17 17