Intradiscal Pressure, Shear Strain, and Fiber Strain in the Intervertebral Disc Under Combined Loading

Article (PDF Available)inSpine 32(7):748-55 · May 2007with167 Reads
DOI: 10.1097/01.brs.0000259059.90430.c2 · Source: PubMed
Abstract
Finite element study. To investigate intradiscal pressure, shear strain between anulus and adjacent endplates, and fiber strain in the anulus under pure and combined moments. Concerning anulus failures such as fissures and disc prolapses, the mechanical response of the intervertebral disc during combined load situations is still not well understood. A 3-dimensional, nonlinear finite element model of a lumbar spinal segment L4-L5 was used. Pure unconstraint moments of 7.5 Nm in all anatomic planes with and without an axial preload of 500 N were applied to the upper vertebral body. The load direction was incrementally changed with an angle of 15 degrees between the 3 anatomic planes to realize not only moments in the principle motion planes but also moment combinations. Intradiscal pressure was highest in flexion and lowest in lateral bending. Load combinations did not increase the pressure. A combination of lateral bending plus flexion or lateral bending plus extension strongly increased the maximum shear strains. Lateral bending plus axial rotation yielded the highest increase in fiber strains, followed by axial rotation plus flexion or axial rotation plus extension. The highest shear and fiber strains were both located posterolaterally. An additional axial preload tended to increase the pressure, the shear, and fiber strains essentially for all load scenarios. Combined moments seem to lead to higher stresses in the disc, especially posterolaterally. This region might be more susceptible to disc failure and prolapses. These results may help clinicians better understand the mechanical causes of disc prolapses and may also be valuable in developing preventive clinical strategies and postoperative treatments.

Figures

SPINE Volume 32, Number 7, pp 748–755
©2007, Lippincott Williams & Wilkins, Inc.
Intradiscal Pressure, Shear Strain, and Fiber Strain in
the Intervertebral Disc Under Combined Loading
Hendrik Schmidt, PhD, Annette Kettler, MD, Frank Heuer, MS, Ulrich Simon, PhD,
Lutz Claes, PhD, and Hans-Joachim Wilke, PhD
Study Design. Finite element study.
Objective. To investigate intradiscal pressure, shear
strain between anulus and adjacent endplates, and fiber
strain in the anulus under pure and combined moments.
Summary of Background Data. Concerning anulus
failures such as fissures and disc prolapses, the mechan-
ical response of the intervertebral disc during combined
load situations is still not well understood.
Methods. A 3-dimensional, nonlinear finite element
model of a lumbar spinal segment L4 –L5 was used. Pure
unconstraint moments of 7.5 Nm in all anatomic planes
with and without an axial preload of 500 N were applied
to the upper vertebral body. The load direction was incre-
mentally changed with an angle of 15° between the 3
anatomic planes to realize not only moments in the prin-
ciple motion planes but also moment combinations.
Results. Intradiscal pressure was highest in flexion
and lowest in lateral bending. Load combinations did not
increase the pressure. A combination of lateral bending
plus flexion or lateral bending plus extension strongly
increased the maximum shear strains. Lateral bending
plus axial rotation yielded the highest increase in fiber
strains, followed by axial rotation plus flexion or axial
rotation plus extension. The highest shear and fiber
strains were both located posterolaterally. An additional
axial preload tended to increase the pressure, the shear,
and fiber strains essentially for all load scenarios.
Conclusions. Combined moments seem to lead to
higher stresses in the disc, especially posterolaterally.
This region might be more susceptible to disc failure and
prolapses. These results may help clinicians better under-
stand the mechanical causes of disc prolapses and may
also be valuable in developing preventive clinical strate-
gies and postoperative treatments.
Key words: combined loading, finite element analysis,
disc prolapse, anulus failure, intervertebral disc. Spine
2007;32:748 –755
Approximately 70% of the population in industrialized
countries experience back pain at least once in the course
of their lives.
1
Patients require long-term care, and their
quality of life is often limited. Acute episodes of low back
pain can be caused by disc prolapses, a multifactorial
process in which the mechanical environment as well as
age and degeneration effects have an impact. Adams and
Hutton, for example, found that high loading can distort
the lamellae in the anulus forming radial fissures so that
prolapses may occur.
2
In the past, many in vivo and in vitro studies were
performed to describe the potential overloading of the
spine. It was often demonstrated that a disc may prolapse
under certain load combinations of flexion, lateral bend-
ing, axial rotation, and axial compression.
2–7
These
combinations may produce high pressures in the nucleus
and local regions of large stresses in the anulus,
8
with the
highest stresses found in the posterolateral region.
9
In
contrast, an axial rotation alone does not seem to over-
load the intervertebral disc. This may be due to the facet
joints, which transfer a substantial part of the load and
thus limit the movement of the disc.
10
In experimental in vivo or in vitro investigations, only
certain parameters can be measured, e.g., the relative
movement between 2 adjacent vertebrae, disc bulges, or
the intradiscal pressure in individual areas of the inter-
vertebral disc. Other parameters, such as strains or
stresses in different regions of the intervertebral disc, can-
not be characterized completely in experiments. In the
past, it was shown that finite element (FE) models were
helpful to quantify these parameters. However, most of
the previous FE studies were only used to simulate pure
moments in 1 of the 3 anatomic main planes, simulating
flexion-extension, lateral bending, and axial rotation,
partially combined with an axial compression. However,
in the physiologic situation, a state of complex loading
exists. Only few groups analyzed the disc behavior under
predefined load combinations.
11,12
The investigators ex-
amined the mechanical behavior of the disc under spe-
cific load combinations, known to result in disc pro-
lapses in vitro: combinations of flexion or extension plus
lateral bending and axial rotation. They found that the
maximum fiber strains occurred in the posterior and pos-
terolateral anulus and reasoned that disc failure predom-
inantly occur in these areas. However, in these FE stud-
ies, only a few load situations were investigated. Other
load combinations could lead to higher internal fiber and
shear strains in the anulus than those observed combina-
tions. Furthermore, the influence of parameters, such as
shear and fiber strains in the anulus on disc failure, has
not yet been extensively investigated.
From the Institute of Orthopaedic Research and Biomechanics, Uni-
versity of Ulm, Ulm, Germany.
Acknowledgment date: March 3, 2006. First revision date: June 8,
2006. Acceptance date: August 9, 2006.
Supported by the Deutsche Forschungsgemeinschaft (WI 1352/6-1),
Bonn, Germany.
The manuscript submitted does not contain information about medical
device(s)/drug(s).
Federal funds were received in support of this work. No benefits in any
form have been or will be received from a commercial party related
directly or indirectly to the subject of this manuscript.
Address correspondence and reprint requests to Hans-Joachim Wilke,
PhD, Institute of Orthopaedic Research and Biomechanics, Helm-
holtzstrasse 14, D-89081 Ulm, Germany; E-mail: hans-joachim.wilke@
uni-ulm.de
748
Therefore, the aim of this study was to find load com-
binations, which would lead to the highest internal
stresses in the intervertebral disc and to determine the
location in which the highest stresses occurred. To esti-
mate the mechanical behavior of the disc, the shear and
fiber strains in the anulus as well as the intradiscal pres-
sure in the nucleus were determined.
Materials and Methods
FE Model. A nonlinear, 3-dimensional, symmetric FE model
of a human lumbar spinal segment L4 –L5 was generated based
on volume reconstruction of a high-resolution computer to-
mography scan (Philips MX 8000 IPT device) having a lateral
resolution of 0.49 mm with a slice thickness of 0.75 mm (Figure
1). Additional magnetic resonance imaging (Magnetom Sym-
phony Maestro Class, Siemens, Germany) and histologic ob-
servations were conducted defining the soft tissue geometries.
The reconstructed volume data set was transferred into a FE
package (ANSYS 10.0; Swanson Analysis, Houston, PA) and
subsequently meshed. The modeled vertebrae included cortical
bone, cancellous bone, bony endplates, and posterior struc-
tures with facet joints. These components and the intervening
intervertebral disc with the cartilaginous endplate were meshed
using 8-node isoparametric solid elements. The collagen fibers
of the anulus and the 7 spinal ligaments, the anterior and pos-
terior longitudinal ligament, flaval, supraspinous, interspinous,
transversal, and capsular ligaments were represented by 3-di-
mensional, unidirectional spring elements. The contact be-
tween the facet joints was simulated by surface-to-surface con-
tact elements without friction.
The modeled intervertebral disc consisted of the nucleus
pulposus and the anulus, whereas the anulus was assumed to be
composed of a homogeneous ground substance reinforced by a
collagen fiber network (Figure 1). Eight crisscross fiber layers
were defined in radial direction. The angulations of the fibers
varied from 24° to the horizontal plane ventrally to 46° at
the dorsal side according to histologic findings.
13,14
The rela
-
tive volume content of the fibers with respect to the surround-
ing ground substance was assumed to vary from 23% at the
outer layer to 5% at the inner fiber layer.
11
Material properties of the different tissues were extracted
from the literature (Table 1). The fluid-like behavior of the
nucleus and the hyperelastic properties of the anulus ground
substance were both modeled using an isotropic, incompress-
ible, hyperelastic Mooney-Rivlin formulation.
15
The stress-
strain behavior of the anular collagen fibers were described by
a nonlinear function, which was obtained from previous re-
ports.
16
Since outer lamellae behave stiffer than inner lamel
-
lae,
17
the fibers in different anulus layers were weighted (out
-
ermost layers 1–2, 1.0; layers 3– 4, 0.9; layers 5– 6, 0.75;
Figure 1. Midsagittal cut through
the 3-dimensional, nonlinear FE
model of the complete functional
spinal unit L4–L5 and the inter-
vertebral disc with endplates.
Table 1. Material Properties of the Different Tissues in the Finite Element Model
Material Young’s Moduli (MPa) Poisson’s Ratio Reference
Cortical bone E
xx
11,300
xy
0.484
E
yy
11,300
yz
0.203
E
zz
22,000
xz
0.203
Lu et al
11
G
xy
3800
G
yz
5400
G
xz
5400
Cancellous bone E
xx
140
xy
0.450
E
yy
140
yz
0.315
E
zz
200
xz
0.315
Lu et al
11
G
xy
48.3
G
yz
48.3
G
xz
48.3
Posterior bony elements E 3500
0.25 Shirazi-Adl et al
16
Bony endplate E 4000 to 12,000
0.3 Edwards et al
50
Cartilaginous endplate E 23.8
0.4 Lu et al
11
Anulus ground substance Mooney-Rivlin c
1
0.18, c
2
0.045
0.45 Schmidt et al
15
Anulus fibers Stress-strain curve determined by Shirazi-Adl
et al
16
Nucleus pulposus Mooney-Rivlin c
1
0.12, c
2
0.03
0.4999 Smit
51
749Intradiscal Pressure, Shear Strain, and Fiber Strain
Schmidt et al
innermost layers 7– 8, 0.65). Force-deflection curves were ob-
tained to represent spinal ligament behavior.
18
The facet carti
-
lage was assumed to be multilinear elastic in compression.
17
Calibration. For the calibration process, in vitro data from
previously reported studies were used, including range of mo-
tion (rotation) and intradiscal pressure.
19,20
In these experi
-
ments, 6 specimens were tested in the intact state. Afterwards,
the anatomy was successively reduced, including the different
ligaments, facet joints, and nucleus. In the intact and in all
defect stages, the segment was tested with pure moments of 1,
2.5, 5, 7.5, and 10 Nm in all load directions. Before the exper-
iments, specimens were exposed for 15 minutes to 500 N axial
compression to reduce the water content of specimens
21
to
avoid abnormal height water content.
The FE model, whose geometry was based on 1 of the 6
tested specimens, was calibrated with these data by adding
these structures in the opposite way, starting with an isolated
anulus to which only the vertebral bodies were added. The
other different anatomic structures were cumulatively added.
In each calibration step, the material property of the added
structure was modified, so that the FE model fulfilled the ex-
perimentally obtained range of motion and intradiscal pressure
data.
22
Anulus. In a previous study,
15
a calibration method was
developed, which considers the individual contribution of the
fibers and the ground substance. The stiffness of the fibers was
varied to approximate the Young’s modulus of the ground
substance in order to fulfill the required range of motion.
Nucleus Pulposus. A parametric study was performed on the
nucleus material properties. Young’s modulus was varied in a
range of 0.1 to 4 MPa.
24,25
Vertebral Arches With Facet Joints. The orientation of the
facet joints was varied in a parametric study in order to obtain
the influence on the motion response. The final angle is within
the reported range.
26,27
Ligaments. The force-deflection behavior of all ligaments
was sequentially computed. Because of the 5 moment magni-
tudes, 6 points were determined and subsequently intercon-
nected by a spline function describing continuous force deflec-
tion behavior.
Validation. For this study, the results of the complete as-
sembled FE model were additionally compared with intra-
discal pressure data from previously performed experimen-
tal studies.
19
Loading and Boundary Conditions. The inferior endplate
of the lower vertebral body was rigidly fixed. Pure uncon-
strained moments of 7.5 Nm were applied to the superior end-
plate of the upper vertebral body, as it has been recommended.
28
The loading direction was incrementally changed by an angle
of 15° between the different anatomic planes to realize not only
pure moments in flexion/extension, lateral bending and axial
rotation but also load combinations of flexion plus lateral bend-
ing, flexion plus axial rotation, extension plus lateral bending,
extension plus axial rotation, and lateral bending plus axial rota-
tion. The line of action for the resulting moment between 2 ana-
tomic planes was an oblique spatial axis. The applied moment
about this axis was always 7.5 Nm.
Subsequently, these load scenarios were additionally com-
bined with an axial compression of 500 N simulating upper
body weight. This load was applied as if it was a follower
load.
29
Thus, the load path passed the center of the vertebral
bodies and did not additionally create any significant bending
moment. For the FE model, nonlinear large deformations were
used for calculation. To ensure the convergence, 6 to 10 sub-
steps were iteratively determined using the “Newton-
Raphson” approach.
Data Analysis. The following parameters were considered to
be the most important to estimate internal stress behavior of
the intervertebral disc:
The intradiscal pressure in the nucleus was determined as
one third of the trace of the stress tensor, i.e., the mean of the 3
normal stresses. This was necessary since the nucleus was gen-
erated with solid elements.
The shear strains between the anulus and the adjacent end-
plates were determined as a vector summation of the shear
strain components
xz
and
yz
. Thereby, x was defined in pos
-
teroanterior, y in lateral, and z in longitudinal direction. It was
found in radiographic studies that the outer anulus separate
from the adjacent vertebral bodies and produce peripheral rim
lesions.
30,31
We assumed that these failures mainly caused by a
resulting shear load.
The tensile strains in the normal direction of the fibers,
which may lead to fiber disruptions and initiate radial tears.
2
Results
Validation
Both, the numerical and the in vitro curves represent a
similar nonlinear curve (Figure 2). Under a moment of
7.5 Nm, flexion showed with 5.9° the largest range of
motion (in vitro, 6.1°), followed by lateral bending with
5.3° (in vitro, 5.15), extension with 4.5° (in vitro, 4.1°),
and axial rotation with 2.5° (2.7°).
Intradiscal Pressure
The intradiscal pressure was highest in flexion (0.35
MPa), followed by extension (0.18 MPa), axial rotation
(0.16 MPa), and lateral bending (0.14 MPa) (Figure 3). A
bending or torsion moment about an oblique axis did not
strongly increase the nucleus pressure compared with the
same moment applied in a principle direction. For all
load scenarios, the additionally applied follower load
resulted in an increase by an average offset value of 0.34
MPa.
Shear Strains
For all load scenarios, the maximum shear strain was
found to be located between the anulus and the inferior
endplate. Under pure moments, lateral bending gener-
ated the largest shear strains (39.7%), while axial rota-
tion (32.8%) led to the smallest shear strains (Figure 4).
The maximum shear strains for lateral bending occurred
at the ipsilateral side of the anulus (Figure 5).
A combination of lateral bending plus extension and
lateral bending plus flexion produced a substantial in-
crease in shear strains (up to 44.7%) (Figure 4). They
occurred at the posterolateral region of the anulus (Fig-
ure 6). In contrast, a combination of right axial rotation
750 Spine
Volume 32
Number 7
2007
plus lateral bending and axial rotation plus extension
showed a large decrease in shear strains and occurred at
the lateral and posterolateral region of the anulus, re-
spectively. The presence of a follower load tended to
increase the shear strains for all load scenarios by an
average offset value of 5% but did not change the loca-
tion of the maximum shear strain.
Fiber Strains
Except axial rotation, the maximum fiber strains in-
creased toward the innermost fiber layer (Figures 7 and
8). Under pure moments, it was observed that axial ro-
tation generated the largest tensile strains in the collagen
fibers (11.9%), while extension led to the smallest fiber
strains (5.9%). Axial rotation showed maximum tensile
strains posterolaterally. Only the fibers, which were ori-
ented in direction of the applied moment, underwent
tensile strains.
Lateral bending in combination with left axial rota-
tion yielded the highest increase in fiber strains (19.8%)
(Figure 7). A load combination of lateral bending plus
extension showed the strongest decrease in fiber strains
(down to 1.5%). The maximum strains for lateral bend-
ing plus axial rotation occurred at the posterolateral re-
gion (Figure 8). For all load combinations, the fibers,
which run from the inferior endplate to the superior end-
plate in a clockwise direction, underwent tensile strains.
Figure 2. Comparison between finite element (FE) analysis and in vitro data for validation purposes: Intradiscal pressure (IDP) versus
range of motion (RoM) for flexion, extension, lateral bending and axial rotation under pure moments of 1, 2.5, 5, 7.5, and 10 Nm (symbols).
Figure 3. Intradiscal pressure (IDP) in the nucleus under pure and combined moments. The pressure is diagramed in cylindrical
coordinates: IDP is shown radially and the applied load in the circumference. Left: axial rotation plus flexion and axial rotation plus
extension; middle: lateral bending plus flexion and lateral bending plus extension; right: lateral bending plus right and left axial rotation.
751Intradiscal Pressure, Shear Strain, and Fiber Strain
Schmidt et al
The fibers running in the other direction were all in com-
pression.
The additionally applied follower load resulted in an
increase in the maximum fiber strains for all load scenar-
ios, by an average offset value of 3.3% but did also not
change the location of the maximum fiber strain.
Discussion
In the present study, a 3-dimensional, nonlinear FE
model was used to determine the load combinations,
which led to the highest internal loads of the interverte-
bral disc. The results of this study yielded some general
rules, which might be important in clarifying the cause of
anulus failure and disc prolapses.
Validation
The predicted relationship between range of motion and
intradiscal pressure generated by the complete assembled
FE model showed a good agreement with the experimen-
tally determined in vitro data (Figure 2).
Currently, there is a paucity of in vitro data concern-
ing both fiber and shear strain measurements, due to the
difficulty in obtaining these measurements without dam-
aging or destroying the intact discs. Therefore, it was not
possible to directly validate the fiber and shear strains of
the anulus in the FE model. However, to ensure the ac-
curacy of the FE model, the disc behavior was compared
with measurements of Shah et al, who determined cir-
cumferential strains at the anulus surface in flexion and
extension.
32
They reported that the tangential surface
strain was highest at the posterior disc for flexion and at
the anterior disc for extension. Since the fibers in our
model reflect this behavior quite well, we concluded that
the fiber strains were in a conceivable range. Tencer and
Mayer
33
computed in an experimental kinematical ap
-
proach that the maximum strains for lateral bending oc-
curred at the contralateral side of the anulus, which also
was in good agreement with the presented results. How-
ever, a comparison of the fiber strains in axial rotation
indicated a disagreement.
Unfortunately, we could not find any literature to val-
idate our shear strains. Since the FE model showed a
good agreement with the range of motion, we concluded
that the shear strains were in a conceivable range. How-
ever, these findings should be interpreted with care.
Intradiscal Pressure
An overload of the intervertebral disc during combined
loading considering only the intradiscal pressure does
not seem to be given. Furthermore, the intradiscal pres-
sure seems to be dependent on the range of motion.
19
Both were highest in flexion and smallest in lateral bend-
ing and did not show a maximum under combined load
scenarios. Previously performed in vitro experiments
showed a large range of intradiscal pressures.
9,34–38
Yet
the results of the presented study showed similar tenden-
cies, especially compared with in vitro pressure measure-
ments of McNally et al,
36
who investigated the pressure
distribution in the intervertebral disc under a compres-
sion load of 500 N. Similar to the presented study, the
authors found that the intradiscal pressure increased by
0.5 MPa.
Fiber Strains
It was shown that, under pure moments, axial rotation
generated the largest tensile strains in the fibers. It seems
to be contrary to a previous in vitro study.
39
There it was
stated that the intervertebral disc is protected by the ap-
ophyseal joints against axial rotation. However, the fiber
strains would not substantially change when higher mo-
ments in axial rotation are applied (7.5 Nm, 11.9%; 10
Nm, 12.2%), while moments in flexion (7.5 Nm, 7.2%;
10 Nm, 9.2%), extension (7.5 Nm, 5.9%; 10 Nm, 8.3%)
and lateral bending (7.5 Nm, 8.9%; 10 Nm, 12.8%)
strongly increase the fiber strains. In axial rotation, from
7.5 Nm upwards, the fibers are protected by the facet
joints. This correlates with a previous numerical study by
Figure 4. Maximum shear strains in the anulus under combined
loads: axial rotation plus flexion (AR(L) Flex), axial rotation plus
extension (AR(L) Ext), lateral bending plus flexion (LB Flex),
lateral bending plus extension (LB Ext); lateral bending plus left
axial rotation (LB AR(L)), and lateral bending plus right axial
rotation (LB AR(R)).
Figure 5. Locations of predicted shear strains in the anulus under
pure moments: flexion, extension, lateral bending, and left axial
rotation (AR(L)). Regions of the anulus, which were larger than
90% of this peak strain, were depicted as hatched areas.
752 Spine
Volume 32
Number 7
2007
Shirazi-Adl
12
and approves in vitro findings of Adams
and Hutton.
39
The fibers underwent a maximum tensile strain during
load combinations of axial rotation with lateral bending
and axial rotation with flexion. These load conditions
essentially affect the innermost anulus layer at the pos-
terolateral location. This was comparable with previ-
ously reported FE studies.
11,12,40
They suggested that
lifting combined with bending and axial rotation could
be responsible for initiating fiber failure at the inner anu-
lus layer in the posterior and posterolateral region. Dur-
ing an optimization study,
15
it was found that anterior
fibers need to be 32% stiffer than posterolateral fibers to
fulfill the in vitro flexibility of the anulus.
20
These results
may explain the high level of tensile strains and therefore
eventual ruptures of fiber in this region. Under pure mo-
ments, axial rotation generated the largest fiber strains,
whereas extension resulted in the smallest strains. It
should be noted that the range of motion at the lumbar
segment was higher in extension than in axial rotation.
The strains in the anulus fibers increased essentially
when an additional follower load was applied. In exper-
imental studies, it was found that the ultimate tensile
strain of collagenous fibers is 10% to 25%.
41–43
This
suggests that, under lateral bending plus left axial rota-
tion and axial rotation plus flexion even without a fol-
lower load, disc fibers in the posterolateral region may be
susceptible to rupture.
Shear Strains
It was found that the load combinations, which caused a
strong increase of the fiber strains, did not also lead to
the largest increase of the shear strains. The anulus un-
derwent a maximum shear strain exposed to lateral
bending plus flexion or extension. In comparison to the
fiber strains, the maximum shear strains occurred also
posterolaterally, which is consistent with previous find-
ings.
44,45
Furthermore, the maximum shear strains were
located caudally close to the endplate. This suggests that
tears could occur at the interface to the lower rather than
to the upper endplate. Thus, according to these results, a
disc prolapse could be located posterolaterally at the in-
ferior endplate, which would be consistent with previous
reports.
46
Limitations of the FE Analysis
During the segmentation and reconstruction process, the
geometries of both vertebrae were smoothed to limit the
number of elements.
15
More anatomic details would re
-
Figure 6. Locations of shear
strains in the anulus under com-
bined moments: axial rotation
plus flexion (AR(L) Flex), axial
rotation plus extension (AR(L)
Ext), lateral bending plus flexion
(LB Flex), lateral bending plus
extension (LB Ext); lateral
bending plus left axial rotation
(LB AR(L)) and lateral bending
plus right axial rotation (LB
AR(R)). Regions of the anulus,
which were larger than 90% of
this peak strain, were depicted
as black areas.
Figure 7. Maximum tensile strain in the anulus fibers under pure
(left) and combined (right) loads: axial rotation plus flexion (AR(L)
Flex), axial rotation plus extension (AR(L) Ext), lateral bending
plus flexion (LB Flex), lateral bending plus extension (LB Ext);
lateral bending plus left axial rotation (LB AR(L)) and lateral
bending plus right axial rotation (LB AR(R)).
753Intradiscal Pressure, Shear Strain, and Fiber Strain
Schmidt et al
quire substantially more elements and nodes, including
more degrees of freedom. These additions would have
dramatically increased the computation time. The geom-
etry of the anulus was based on transverse histologic
slices of specimens and magnetic resonance imaging
scans. However, resolution and slice thickness of both
methods were limited.
A variation in geometric parameters, such as disc
height, cross-sectional area of the intervertebral disc, size
and position of the nucleus, fiber network orientation, or
the number of fiber layers, can affect the mechanical be-
havior of the intervertebral disc.
24,47–49
This suggests
that other FE models with different geometries might
lead to different results. However, after careful valida-
tion, all FE models should show at least the same tenden-
cies.
22
Conclusion
The study showed that the anulus is highest strained in
the posterolateral region. This might explain that the
most common location of lumbar disc prolapse occur in
this location. A disc may prolapse under a combination
of axial rotation plus lateral bending, axial rotation plus
flexion or lateral bending plus flexion or extension. This
risk will be significantly increased when an axial load is
also added. For clinical practice, this would mean that
patients should avoid load combinations, especially with
lifting tasks.
Key Points
The aim was to find the load combination, which
leads to highest pressure in the nucleus and shear
and fiber strains in the anulus.
A 3-dimensional, calibrated finite-element model
of a functional spinal unit (L4 –L5) was used.
Intradiscal pressure correlated with the magni-
tude of deformation.
The maximum shear and fiber strains occurred
during combined bending moments and were lo-
cated posterolaterally.
Results may help clinicians to better explain the
mechanical cause of disc failure and disc prolapses.
Acknowledgments
The authors thank Dr. B. Willie for editorial assistance.
References
1. Waters TR, Putz-Anderson V, Garg A, et al. Revised NIOSH equation for the
design and evaluation of manual lifting tasks. Ergonomics 1993;36:749 –76.
2. Adams MA, Hutton WC. Gradual disc prolapse. Spine 1985;10:524 –31.
3. Adams MA, Freeman BJ, Morrison HP, et al. Mechanical initiation of inter-
vertebral disc degeneration. Spine 2000;25:1625–36.
4. Adams MA, Hutton WC. Prolapsed intervertebral disc: a hyperflexion in-
jury. 1981 Volvo Award in Basic Science. Spine 1982;7:184–91.
5. McNally DS, Adams MA, Goodship AE. Can intervertebral disc prolapse be
predicted by disc mechanics. Spine 1993;18:1525–30.
6. Gordon SJ, Yang KH, Mayer PJ, et al. Mechanism of disc rupture: a prelim-
inary report. Spine 1991;16:4506.
7. Edwards WT, Ordway NR, Zheng Y, et al. Peak stresses observed in the
posterior lateral anulus. Spine 2001;26:1753–9.
8. McNally DS, Adams MA. Internal intervertebral disc mechanics as revealed
by stress profilometry. Spine 1992;17:66–73.
9. Steffen T, Baramki HG, Rubin R, et al. Lumbar intradiscal pressure mea-
sured in the anterior and posterolateral annular regions during asymmetrical
loading. Clin Biomech (Bristol, Avon) 1998;13:495–505.
10. Adams MA, Hutton WC. The mechanical function of the lumbar apophyseal
joints. Spine 1983;8:327–30.
11. Lu YM, Hutton WC, Gharpuray VM. Do bending, twisting, and diurnal
fluid changes in the disc affect the propensity to prolapse? A viscoelastic finite
element model. Spine 1996;21:2570–9.
12. Shirazi-Adl A. Strain in fibers of a lumbar disc: analysis of the role of lifting
in producing disc prolapse. Spine 1989;14:96–103.
13. Eberlein R, Holzapfel GA, Schulze-Bauer CAJ. An anisotropic constitutive
model for annulus tissue, and enhanced finite element analysis of intact lumbar
disc bodies. Comput Methods Biomech Biomed Eng 2001;4:209 –30.
14. Cassidy JJ, Hiltner A, Baer E. Hierarchical structure of the intervertebral
disc. Connect Tissue Res 1989;23:75–88.
Figure 8. Location of the pre-
dicted tensile strains in the anulus
fibers under pure and combined
moments. The distinguished fiber
layers show the region, in which
the tensile fiber strains were de-
termined larger than 90% of the
maximum determined fiber strain
of each load direction.
754 Spine
Volume 32
Number 7
2007
15. Schmidt H, Heuer F, Simon U, et al. Application of a new calibration method
for a three-dimensional finite element model of a human lumbar annulus
fibrosus. Clin Biomech (Bristol, Avon) 2006;21:337–44.
16. Shirazi-Adl A, Ahmed AM, Shrivastava SC. Mechanical response of a lum-
bar motion segment in axial torque alone and combined with compression.
Spine 1986;11:914–27.
17. Sharma M, Langrana NA, Rodriguez J. Role of ligaments and facets in
lumbar spinal stability. Spine 1995;20:887–900.
18. Pingel TH. Beitrag zur Herleitung und numerischen Realisierung eines math-
ematischen Modells der menschlichen Wirbelsa¨ule. Mitteilungen aus dem
Institut fu¨ r Mechanik 1991.
19. Heuer F, Schmidt H, Claes L, et al. Stepwise reduction of functional spinal
structures increase vertebral translation and intradiscal pressure. J Biomech
2006 [Epub ahead of print].
20. Heuer F, Schmidt H, Klezl Z, et al. Stepwise reduction of functional spinal
structures increase range of motion and change lordosis angle. J Biomech
2007;40:271–80.
21. Adams MA, Dolan P, Hutton WC. The lumbar spine in backward bending.
Spine 1988;13:1019–26.
22. Schmidt H, Heuer F, Drumm J, et al. Application of a calibration method
provides more realistic results for a finite element model of a lumbar spinal
segment. Clin Biomech (Bristol, Avon) in press.
23. Deleted in proof.
24. Goel VK, Monroe BT, Gilbertson LG, et al. Interlaminar shear stresses and
laminae separation in a disc: finite element analysis of the L3–L4 motion
segment subjected to axial compressive loads. Spine 1995;20:689–98.
25. Lavaste F, Skalli W, Robin S, et al. Three-dimensional geometrical and me-
chanical modelling of the lumbar spine. J Biomech 1992;25:1153–64.
26. Masharawi Y, Rothschild B, Dar G, et al. Facet orientation in the thoraco-
lumbar spine: three-dimensional anatomic and biomechanical analysis.
Spine 2004;29:1755–63.
27. Panjabi MM, Oxland T, Takata K, et al. Articular facets of the human spine:
quantitative three-dimensional anatomy. Spine 1993;18:1298–310.
28. Wilke HJ, Wenger K, Claes L. Testing criteria for spinal implants: recom-
mendations for the standardization of in vitro stability testing of spinal
implants. Eur Spine J 1998;7:148–54.
29. Patwardhan AG, Havey RM, Meade KP, et al. A follower load increases the
load-carrying capacity of the lumbar spine in compression. Spine 1999;24:
1003–9.
30. Hilton RC, Ball J, Benn RT. Vertebral end-plate lesions (Schmorl’s nodes) in
the dorsolumbar spine. Ann Rheum Dis 1976;35:127–32.
31. Osti OL, Vernon-Roberts B, Fraser RD. Annular tears and intervertebral disc
degeneration: an experimental study using an animal model. Spine 1990;15:
762–7.
32. Shah JS, Hampson WG, Jayson MI. The distribution of surface strain in the
cadaveric lumbar spine. J Bone Joint Surg Br 1978;60:246–51.
33. Tencer AF, Mayer TG. Soft tissue strain and facet face interaction in the
lumbar intervertebral joint: II. Calculated results and comparison with ex-
perimental data. J Biomech Eng 1983;105:210–5.
34. Adams M, McNally D, Chinn H, et al. Posture and the compressive strength
of the lumbar spine. Clin Biomech 1994:5–14.
35. Adams MA, Hutton WC. The effect of posture on diffusion into lumbar
intervertebral discs. J Anat 1986;147:121–34.
36. McNally DS, Adams MA, Goodship AE. Development and validation of a
new transducer for intradiscal pressure measurement. J Biomed Eng 1992;
14:495–8.
37. Wilke H, Neef P, Hinz B, et al. Intradiscal pressure together with anthropo-
metric data: a data set for the validation of models. Clin Biomech (Bristol,
Avon) 2001;16(suppl 1):111–26.
38. Wilke HJ, Neef P, Caimi M, et al. New in vivo measurements of pressures in
the intervertebral disc in daily life. Spine 1999;24:755–62.
39. Adams MA, Hutton WC. The relevance of torsion to the mechanical de-
rangement of the lumbar spine. Spine 1981;6:241–8.
40. Kim Y. Prediction of peripheral tears in the anulus of the intervertebral disc.
Spine 2000;25:1771–4.
41. Betsch DF, Baer E. Structure and mechanical properties of rat tail tendon.
Biorheology 1980;17:83–94.
42. Haut RC. Age-dependent influence of strain rate on the tensile failure of
rat-tail tendon. J Biomech Eng 1983;105:296–9.
43. Holzapfel GA, Schulze-Bauer CA, Feigl G, et al. Single lamellar mechanics of
the human lumbar anulus fibrosus. Biomech Model Mechanobiol 2005;3:
125–40.
44. Ebeling U, Reulen HJ. Are there typical localisations of lumbar disc hernia-
tions: a prospective study. Acta Neurochir (Wien) 1992;117:143–8.
45. Spangfort EV. The lumbar disc herniation: a computer-aided analysis of
2,504 operations. Acta Orthop Scand Suppl 1972;142:1–95.
46. Dillon WP, Kaseff LG, Knackstedt VE, et al. Computed tomography and
differential diagnosis of the extruded lumbar disc. J Comput Assist Tomogr
1983;7:969–75.
47. Lu YM, Hutton WC, Gharpuray VM. Can variations in intervertebral disc
height affect the mechanical function of the disc. Spine 1996;21:2208–16,
discussion 2217.
48. Natarajan RN, Andersson GB. The influence of lumbar disc height and
cross-sectional area on the mechanical response of the disc to physiologic
loading. Spine 1999;24:1873–81.
49. Shirazi-Adl A. Biomechanics of the lumbar spine in sagittal/lateral moments.
Spine 1994;19:2407–14.
50. Edwards WT, Zheng Y, Ferrara LA, et al. Structural features and thickness
of the vertebral cortex in the thoracolumbar spine. Spine 2001;26:218–25.
51. Smit TH. The Mechanical Significance of the Trabecular Bone Architecture
in a Human Vertebra. Department of Mechanical Engineering. Hamburg-
Harburg: Technische Universita¨ t Hamburg-Harburg, 1996:49 –53.
755Intradiscal Pressure, Shear Strain, and Fiber Strain
Schmidt et al
    • "If synchronously, a ventral flexion is induced, only those 50% of already bent fibers are stressed [44]. Therefore, a combination of axial compression and torsion in a ventrally-flexed position can only rely on 50% of the mechanically-induced stability of the vertebral segment [44], which leads to an increased risk for a discus prolapse [45]. An increased potential for damage can already be expected with shear forces of 150 N [46] and axial rotation torque of 20 Nm [46]. "
    [Show abstract] [Hide abstract] ABSTRACT: For the development of speed strength in professional sports, “specific” strength training in the half or the quarter squat have been recommended. Due to the better lever ratios, higher loads have to be used to induce the necessary training stimuli compared to the deep squat. Therefore, intradiscal pressure and compressive forces on vertebral bodies increase. Calculated compressive forces for the L3/L4 vertebral segment were revealed to be 6–10-fold bodyweight when the half or the quarter squat was performed with 0.8–1.6-fold bodyweight. After 10 weeks of training, physical education students have even been able to lift 3.89-fold bodyweight in the one repetition maximum (1-RM) of the quarter squat. The presented dependence of squatting depth, load and their influence on the spinal column have not been discussed before. A search for relevant scientific literature was conducted using PubMed. Concerns about increased risk of injuries in the deep squat have been disproven by plenty of cross-sectional studies with professional athletes. On the contrary, the comparably supramaximal weight loads in the half and the quarter squat should be regarded as increasing injury risks caused by the higher shear and compressive forces in the vertebral column. Therefore, we come to the conclusion that the half and the quarter squat should not further be recommended.
    Full-text · Article · Jun 2016
    • "Downloaded by [tolerance limits of anterior–posterior shear force for spine are not as well documented as those for compression force, approximately 1,000 N has been recommended as a maximum permissible limit for single exertions (McGill et al. 1998 ). A recent review determined appropriate limits for anterior–posterior shear exposure (Gallagher and Marras 2012), and it was suggested that a 1,000 N shear limit would be recommended for infrequent shear loading 1984; Schmidt et al. 2007). In the current study, the average of compression force values was higher than the NIOSH Action Limit of 3,400 N of compression on the disc, but below the Maximum Permissible Limit of 6,400 N (National Institute for Occupational Safety, Health. "
    [Show abstract] [Hide abstract] ABSTRACT: Large spinal compressive force combined with axial torsional shear force during asymmetric lifting tasks is highly associated with lower-back injury (LBI). The aim of this study was to estimate lumbar spinal loading and muscle forces during symmetric lifting (SL) and asymmetric lifting (AL) tasks using a whole-body musculoskeletal modelling approach. Thirteen healthy males lifted loads of 7 kg and 12 kg under two lifting conditions (SL and AL). Kinematic data and ground reaction force data were collected and then processed by a whole-body musculoskeletal model. The results show AL produced a significantly higher peak lateral shear force as well as greater peak force of psoas major, quadratus lumborum, multifidus, iliocostalis lumborum pars lumborum, longissimus thoracis pars lumborum, and external oblique than SL. The greater lateral shear forces combined with higher muscle force and asymmetrical muscle contractions may have the biomechanical mechanism responsible for the increased risk of LBI during AL.Practitioner summaryEstimating lumbar spinal loading and muscle forces during free-dynamic asymmetric lifting tasks with a whole-body musculoskeletal modelling in OpenSim is the core value of this research. The results show that certain muscle groups are fundamentally responsible for asymmetric movement, thereby producing high lumbar spinal loading and muscle forces, which may increase risks of LBI during asymmetric lifting tasks.
    Full-text · Article · May 2016
    • "E-mail: m.hecimovich@murdoch.edu.au (Schmidt et al., 2007), and bony components such as the pars interarticularis (Chosa, Totoribe, & Tajima, 2004), two common sites of injury in the fast bowler (Hardcastle et al., 1992 ). Bowling technique, specifically excessive trunk movements in the transverse (Burnett et al., 1996; Foster, John, Elliott, Ackland, & Fitch, 1989; Hardcastle et al., 1992) and frontal planes (Bayne et al., 2016; Ranson, Burnett, King, Patel, & O'Sullivan, 2008) also influence lumbar injury in the fast bowler. For example, excessive shoulder counter rotation (SCR) has been linked with abnormalities in the lumbar vertebra and intervertebral disk (Burnett et al., 1996; Foster et al., 1989; Hardcastle et al., 1992), with excessive lateral trunk flexion to the side contralateral to the bowling arm linked with soft tissue and bony lumbar injuries (Bayne et al., 2016; Ranson et al., 2008). "
    [Show abstract] [Hide abstract] ABSTRACT: Introduction: Adolescent fast bowlers are prone to sustaining lumbar injuries. Numerous components have been identified as contributing factors; however, there is limited empirical evidence outlining how the muscles of the lumbopelvic region, which play a vital role in stabilising the spine, function during the bowling action and the influence of such activation on injuries in the fast bowler. Methods: Surface electromyography was utilised to measure the function of the lumbar erector spinae, lumbar multifidus, gluteus medius and gluteus maximus muscles bilaterally during the fast bowling action in a group of 35 cricket fast bowlers aged 12-16 years. Results: Two prominent periods of activation occurred in each of the muscles examined. The period of greatest mean activation in the erector spinae and multifidus occurred near back foot contact (BFC) and within the post-ball-release (BR) phase. The period of greatest mean activation for the gluteus medius and gluteus maximus occurred during phases of ipsilateral foot contact. Discussion: The greatest periods of muscle activation in the paraspinal and gluteal muscles occurred at times where vertical forces were high such as BFC, and in the phases near BR where substantial shear forces are present. Conclusion: The posterior muscles within the lumbopelvic region appear to play a prominent role during the bowling action, specifically when compressive and shear forces are high. Further research is required to substantiate these findings and establish the role of the lumbopelvic muscles in the aetiology of lumbar injury in the cricket fast bowler.
    Full-text · Article · Feb 2016
Show more