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
Approximately 70% of the population in industrialized
countries experience back pain at least once in the course
of their lives.1Patients require long-term care, and their
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
under certain load combinations of flexion, lateral bend-
ing, axial rotation, and axial compression.2–7These
combinations may produce high pressures in the nucleus
and local regions of large stresses in the anulus,8with the
highest stresses found in the posterolateral region.9In
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
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,
in the physiologic situation, a state of complex loading
exists. Only few groups analyzed the disc behavior under
predefined load combinations.11,12The 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
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),
The manuscript submitted does not contain information about medical
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@
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
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
using 8-node isoparametric solid elements. The collagen fibers
of the anulus and the 7 spinal ligaments, the anterior and pos-
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
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.13,14The 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.15The stress-
strain behavior of the anular collagen fibers were described by
a nonlinear function, which was obtained from previous re-
ports.16Since outer lamellae behave stiffer than inner lamel-
lae,17the 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
MaterialYoung’s Moduli (MPa) Poisson’s RatioReference
Cortical boneExx? 11,300
E ? 3500
E ? 4000 to 12,000
E ? 23.8
Mooney-Rivlin c1? 0.18, c2? 0.045
Lu et al11
Lu et al11
Posterior bony elements
Anulus ground substance
? ? 0.25
? ? 0.3
? ? 0.4
? ? 0.45
Shirazi-Adl et al16
Edwards et al50
Lu et al11
Schmidt et al15
Stress-strain curve determined by Shirazi-Adl
Nucleus pulposusMooney-Rivlin c1? 0.12, c2? 0.03
? ? 0.4999
749 Intradiscal 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.18The 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.19,20In 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 specimens21to
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
Anulus. In a previous study,15a 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-
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-
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.29Thus, 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-
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 ?xzand ?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.30,31We 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
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°).
The intradiscal pressure was highest in flexion (0.35
MPa), followed by extension (0.18 MPa), axial rotation
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
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
750Spine•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.
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
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-
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.
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
anulus failure and disc prolapses.
The predicted relationship between range of motion and
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.32They 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
Mayer33computed 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.
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.9,34–38Yet
the results of the presented study showed similar tenden-
cies, especially compared with in vitro pressure measure-
ments of McNally et al,36who 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
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.39There it was
stated that the intervertebral disc is protected by the ap-
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%;
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
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-Adl12and approves in vitro findings of Adams
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.11,12,40They 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,15it was found that anterior
fibers need to be 32% stiffer than posterolateral fibers to
fulfill the in vitro flexibility of the anulus.20These 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%.41–43This
suggests that, under lateral bending plus left axial rota-
tion and axial rotation plus flexion even without a fol-
susceptible to rupture.
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.44,45Furthermore, 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
Limitations of the FE Analysis
During the segmentation and reconstruction process, the
geometries of both vertebrae were smoothed to limit the
number of elements.15More 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
and position of the nucleus, fiber network orientation, or
the number of fiber layers, can affect the mechanical be-
havior of the intervertebral disc.24,47–49This 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-
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
● The aim was to find the load combination, which
leads to highest pressure in the nucleus and shear
and fiber strains in the anulus.
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-
● Results may help clinicians to better explain the
mechanical cause of disc failure and disc prolapses.
The authors thank Dr. B. Willie for editorial assistance.
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dicted tensile strains in the anulus
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termined larger than 90% of the
maximum determined fiber strain
of each load direction.
754Spine•Volume 32•Number 7•2007
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