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Chapter 11 Finite Element Analysis 173
CADAVERIC AND FE MODEL COMPARISON
C
Intact right rotation (cadaveric)
Intact right rotation (FE model)
Spinal segment
Angular displacement (degrees)
CADAVERIC AND FE MODEL COMPARISON
B
Intact right bending (cadaveric)
Intact right bending (FE model)
Angular displacement (degrees)
CADAVERIC AND FE MODEL COMPARISON
Angular displacement (degrees)
A
experimental testing and the FE model were compared across
L3–S1, L3–L4, L4–L5, and L5–S1 segments. It was found that
the FE model predicted angular displacements across the
segments falling within one standard deviation of the experimental data (Fig. 11.6).
Finite Element Model of the Cervical Spine
A full cervical spine (C1–C7) computational model was
developed that involved the following steps.
22
20
18
16
14
12
10
–2
–4
–6
–8
–10
–12
8
6
4
2
0
L3-S1
Flexion
Extension
L3-L4
Spinal segment
Intact flexion (cadaveric)
Intact flexion (FE model)
Intact extension (cadaveric)
Intact extension (FE model)
L4-L5 L5-S1
Conversion of CT and MRI Scans to 3D Solid Model
To construct the geometry of the cervical spine, CT scan
images of a woman (25 years old) without any abnormalities
with 1-mm slice thickness were obtained from the radiography
department of University of Toledo Medical School. Mimics
13.1 soware package (Materialise) was used to construct the
required 3D structures. For the CT images obtained, bone
contrasting and thresholding procedures were done to each
bone part, and related masks were developed. en, by utilizing the region growing tool, the initial geometry was developed
(Fig. 11.7). Smoothing, wrapping, and ltering functions were
executed to obtain good-quality geometry. A similar procedure was followed to obtain 3D structures of ve intervertebral
discs (C23, C34, C45, C56, and C67) from MRI scans.
Meshing
Each individual 3D structure was imported into the Iowa FE
Mesh soware for creating the mesh structure. A series of
building blocks was constructed around the 3D structure,
assigned a desired mesh density, and projected onto the
surface representation, creating a 3D FE model. Finally, the
mesh quality module in the soware was used to evaluate, and
thus develop, the high-quality mesh for the model. Fig. 11.8
shows the meshing procedure for C3 vertebra.
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I
14
12
10
8
6
4
2
0
–2
–4
–6
–8
–10
–12
–14
10
8
6
4
2
0
–2
–4
–6
–8
–10
FIG. 11.6 (A) Comparison of the experimental and nite element (FE)
model results for exion and extension in response to a 9-Nm pure
moment. (B) Experimental and FE model results are compared in left and
right bending in response to a 9-Nm pure moment. (C) Experimental and FE
model results are compared in left and right rotation in response to a 9 Nm
pure moment.
Right bending
Left bending
L3-S1 L3-L4
Spinal segment
Right rotation
Left rotation
L3-S1 L3-L4
Intact left bending (cadaveric)
Intact left bending (FE model)
L4-L5 L5-S1
Intact left rotation (cadaveric)
Intact left rotation (FE model)
L4-L5 L5-S1
Finite Element Analysis (Using Abaqus Version 6.11)
Abaqus soware was used for the FEA. Meshed parts were
imported into this soware for FEA. Ligament insertion points
and material properties of all of the so and hard tissues
were extracted from literature.
18a
Finally, assembling all of
these parts and assigning their respective material properties
developed the three-dimensional nonlinear full cervical spine
FE model.
e intact model contained 217,366 nodes and 181,336
elements. e global coordinate system of the model (X, Y,
and Z) was oriented in such a way that the positive Y is from
anterior to posterior of the spine, positive X is from right to le
of the spine, and positive Z is from bottom to top of the spine.
Vertebral Body and Posterior Bone
Similar to the lumbar model, the cervical vertebral body consists of a thin cortical shell (0.5 mm of thickness) surrounding
a soer cancellous core. e posterior region was assigned
attributes, which lay between those of the cortical and cancellous regions. ree-dimensional, isoparametric solid elements
(C3D8) were used to dene the osseous geometry.
Facet Joints
A contact formulation was used to dene the contact pattern
between articulating surfaces in facet joints with an initial gap
of 0.5 mm based on CT imaging and dissection procedures.
e contact was dened with an exponentially increasing
modulus as the gap distance between the inferior and superior
facets decreased, simulating the presence of cartilage in the
facet region. e facets were oriented at approximately 45
174 BASIC SCIENCE
C
D
A
FIG. 11.7 Visualization module of Mimics version 13.1 (Materialise). (A–C) Frontal, axial, and sagittal scan views,
respectively, in which bone contrasting, thresholding, and masking were performed for the computed
tomographic slices. (D) Three-dimensional structures developed by performing the smoothing and ltering
options.
B
FIG. 11.8 Meshing procedure for the C3 vertebra. The left image depicts the three-dimensional C3 vertebra,
the center image shows the constructed building blocks, and the right image depicts the meshed vertebra,
respectively.
degrees from the horizontal plane, with some variation in the
sagittal plane alignment, according to CT geometry. e facets
were also of varying curvatures from right to le sides, indi-
cating the possibility of varying contact during right or le
loading modalities from the right to le facets.
Intervertebral Disc and Luschka’s Joints
e anulus brosus was modeled as a composite conguration
in which a series of bers simulating the lamellae of the disc
were embedded in a ground substance surrounding a more
gelatinous nucleus region. Each layer of ground substance
contained two alternating layers of bers arranged at ±65
degrees from the transverse plane, with an overall ber content
of 20% of the annular volume assumed. REBAR element type
with no-compression option was used to dene the bers.
Brick elements were used to model ground substance and the
nucleus pulposis was dened as incompressible uid.
Luschka’s joints were modeled as well in the cervical discs.
ese were simulated around the area of the uncinate processes and the anulus horizontal layers around the uncinate
processes.
Ligaments
e ligaments of the lower cervical spine that were modeled
include the anterior longitudinal ligament (ALL), posterior
longitudinal ligament (PLL), interspinous ligament (ISL), ligamentum avum (LF), and the capsular ligaments (CAPs). e
alar ligament (AL), transverse ligament (TL), anterior and
posterior atlantoaxial ligaments (AT-AX, PAT-AX) were
modeled for the upper cervical spine. e ligaments were
modeled using three-dimensional truss elements with hypoelastic material behavior.
Fig. 11.9 shows a 3D view of an FE model of the C1–C7
spine and all its components. Material properties and
Chapter 11 Finite Element Analysis 175
Transverse
Spinous
process
C1
C2
Intervertebral
Vertebral body
FIG. 11.9 Finite element model of the ligamentous C1–C7 cervical spine.
disc
Facet joint
C7
C5
C6
C3
C4
process
Uncinate
process
cross-sectional areas used in dening the various entities in
the C1–C7 model are summarized in Table 11.3. ese were
chosen based on values published in the literature and were
assumed to be homogeneous and isotropic.
7
Application of the Finite Element Model of the Spine
One of the main advantages of FE modeling of the spine is its
extensive application in simulating the eects of various
trauma and spinal disorders on the biomechanics of the spine.
Numerous studies have simulated dierent spinal injuries and
compared various biomechanical parameters, such as angular
motion and stress distribution across degenerated and adjacent segments, between intact and injured spine models. e
outcomes of such analysis have well served engineers in
coming up with innovative ideas and solutions in the design
of suitable implants to address the pain and restore to normal
the biomechanics of the damaged segment. Implants are useful
in treatment of spinal injuries when conservative therapies fail
to reduce the pain and restore the patient to a normal daily
routine. Invasive surgeries aim to remove the pain-causing
structures, stabilize the segment, and correct bone failure due
to trauma or disease.
Once the FE model of the intact spine is created, it can be
easily modied to simulate dierent injuries by various techniques, such as removing certain elements (e.g., facetectomy,
laminectomy), changing the material properties (e.g., laxity in
ligaments), or modifying the geometry (disc herniation and
degeneration).
For example, spinal stenosis is a progressive degenerative
condition that occurs when the articulating facet joints become
arthritic and no longer provide necessary stability to the
spine. e arthritic facets become inamed and osteophytic
TABLE 11.3 Element Types and Material Properties for Finite Element
Model of Intact C1–C7 Cervical Spine
Young’s
Element Group
Name
Cortical bone C3D8 10,000 0.3 –
Cancellous bone C3D8 450 0.25 –
Posterior bone C3D8 3500 0.25 –
Anulus ground
substance
Anulus bers REBAR – 0.45 –
Nucleus
pulposus
ALL T3D2
PLL T3D2
LF T3D2
ISL T3D2
CAP T3D2 15 (20-40%)
TL T3D2 20 0.3 18.0
AL T3D2
AT-AX T3D2
PAT- A X T3D2
AL, alar ligament; ALL, anterior longitudinal ligament; AT-AX, anterior atlantoaxial
ligament; CAP, capsular ligament; ISL, interspinous ligament; LF, ligamentum avum;
PAT-AX, posterior atlantoaxial ligament; PLL, posterior longitudinal ligament;
TL, transverse ligament.
Element
Typ e
C3D8 4.2 0.25 –
C3D8H 1 0.4999 –
Modulus
(MPa)
15 (<12%)
30 (>12%)
10 (<12%)
20 (>12%)
7 (<12%)
30 (>12%)
5(<25%)
10 (>25%)
30 (>40%)
3.0(<17%)
8.5(>17%)
0.2(<17%)
1.25 (>17%)
6.0(<17%)
10.0 (>17%)
Poisson’s
Ratio
0.3 33.0
0.3 33.0
0.3 50.1
0.3 13.0
0.3 46.6
0.3 22.0
0.3 5.0
0.3 5.0
Cross-sectional
Area (mm2)
(produce bony spurs), resulting in irritation and impingement
of nearby nerves, leading to clinical symptoms. e current
nonconservative treatment for spinal stenosis is surgical
decompression and spinal fusion with instrumentation to
achieve spinal stability and symptom relief. Decompression
is a surgical procedure, which is performed to alleviate pain
caused by pinched nerves (neural impingement). e surgical
procedure for decompression includes removal of part of the
lamina (laminectomy), spinous process, facets (facetectomy),
ligaments, and/or sometimes part of the intervertebral disc
(microdiscectomy).
Although clinical studies have shown that decompression
surgery enhances neurologic recovery, pain relief, and mobility, signicant destabilization of the spinal motion segment
is seen aer decompression, especially if the facet joint is
removed.
Addition of a posterior fusion system, including pedicle
screws interconnected with a rigid rod, is a common procedure to restore the stability of the aected segment.
ough fusion is able to restabilize the implanted segment,
it can result in accelerated degeneration of the adjacent motion
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176 BASIC SCIENCE
segment and morbidity from muscle stripping. Fig. 11.8 shows
an L3–S1 model of the spine with a fusion system at the
L4–L5 level.
Clinical Application of the Finite Element Models of the Spine
FE analysis has become a cost-eective and ecient means to
predict the biomechanics of the spine under physiologic and
pathologic conditions. While useful, the model is not without
limitations due to the constraints of a biologic system and its
associated properties being modeled by a digital representation. e material properties of the ligaments (supraspinous,
interspinous, ligamentum avum, and so on) were obtained
from the literature, while the intervertebral disc was modeled
as a homogeneous composite ground substance. It can be
inferred that the data used to generate the models can be
thought of as an “average” of the normal population, just as
reference ranges are for determining the upper and lower
threshold of certain markers in routine bloodwork.
FE models are based on a number of assumptions, such as
the fact that the generated models should apply equally to all
members of a population. In clinical practice, this does not
oen hold true. Just as individual patients may have varia-
tions in their spine anatomy, the rate of degeneration and the
impact of degenerative processes may vary from patient to
patient, making generalizations about the “best” treatment for
a particular type of spinal pathology far from simple. Oen in
clinical practice, patients with a similar degree of degenerative
pathology may have widely dierent clinical manifestations or,
in some cases, may be completely asymptomatic. e challenge
in making decisions with patients in regard to their pathology
rests on the ability of the clinician to integrate biomechanical data derived from FE models, the radiographic data, and
the patient’s clinical symptoms. us, it becomes important
to not use computational models alone to determine the
appropriate treatment for an individual patient. Additionally, the patients that are seen in practice oen are far down
the degenerative cascade, at which point surgery may only
temporarily alleviate their symptoms before their recurrence
due to scarring, nociceptor hypersensitivity, and/or further
degeneration.
Another limitation of an FE model is that the stability
of the ligamentous spine is less than a spine in vivo due to
absence of the muscles and ligaments. e load-bearing
qualities and structural support aorded by the muscles and
ligaments have been shown to vary greatly, and are inuenced
by the age and quality of bone, the rate of loading, as well as
other physiologic and hereditary characteristics that cannot
be modeled by current computational techniques. In addition,
there have been observations that cadaveric models may show
dierent biomechanical properties based on preparation, and
that the in vivo tissue failure properties may be lower than
that predicted by FE models.19 e importance of the musculature and ligaments and their contribution to spinal stability
is emphasized by the recent surge of interest in minimally
invasive techniques for arthrodesis that minimize muscle
dissection.
Currently, FE models are limited in their ability to evaluate
the spine as a whole, and are instead divided into regions (cervical, thoracic, lumbar) to facilitate analysis of their mechanical
properties. By isolating these segments and subjecting them
to biomechanical analysis, they do not address global spinal
parameters, such as sagittal and coronal balance, which have
become increasingly important in treating spinal pathology.
In addition, the spine’s relationship to the pelvis and pelvic
parameters—such as pelvic tilt, pelvic incidence, and sacral
slope—are currently not addressed by FE models but are used
increasingly by surgeons in making treatment decisions that
impact clinical outcomes and patient satisfaction.
Because FE models are typically based on a specic subject
or an ideal average subject, there is concern regarding the
applicability of FEA to clinical practice. Many studies have
been conducted with the goal of accounting for intersubject
variability as a result of aging and anatomic deformities. For
example, patient-specic FE models have been constructed to
investigate the risk of femoral neck fracture,20 account for
intersubject variability of biomechanical factors in animal
studies,21 and to support the interpretation of clinical results
in follow-up studies. Reggiani et al. reported a preliminary
validation of patient-specic FE models with regard to predicting the subject-specic primary stability of cementless
implants during preoperative planning.
22
Although a need remains for a validated model that
accounts for injury, deformity, or disease, more recent studies
have demonstrated the usefulness of coupling FEA with
patient-specic information from clinical CT scans to mechanistically simulate bone failure. is approach has been validated by numerous groups for the spine and hip, and clinically
has been shown to be signicantly associated with incident
and prevalent fracture in multiple cohorts. A study conducted
by Kopperdahl et al. has further demonstrated clinical integration of FEA through its use of FEA-based vertebral strength
assessments and vertebral trabecular bone mineral density
(BMD) to predict incident vertebral fractures in women.
23
e International Society for Clinical Densitometry (ISCD)
has recently developed new ocial positions for the clinical
use of quantitative CT (QCT)-based FEA of the spine and hip,
specically with regard to the management of osteoporosis in
adults. According to the ISCD, QCT-based FEA can be used
to assess fracture risk, initiate pharmacologic treatment of low
vertebral and femoral strength, as well as monitor age- and
treatment-related changes to bone strength.
24
Perhaps the most important application of FE models in the
spine is their utility in creating medical devices that are intended
to arrest the degenerative cascade. In current clinical practice, a
signicant proportion of spine procedures are centered around
removing oending pathology (laminectomy, facetectomy,
corpectomy, and so on) and fusing the levels of interest using
implants such as rods and pedicle screws. Over time, the inam-
matory cascade that promotes healing fuses the operated levels
while placing stress on the adjacent motion segment. While, in
many cases, the patient’s preoperative symptoms may temporarily improve, symptom recurrence and/or exacerbation in the
future is not uncommon due to accelerating the degenerative
cascade in the adjacent level. e existence of conditions such as
Chapter 11 Finite Element Analysis 177
ROM in extension
“failed back surgery syndrome” (FBSS) and patient dissatisfaction aer repeat fusion surgery suggest that the data used to
create implants and to perform spine surgery are limited in
their ability to truly predict the surgical solution that is ideal
for a particular patient. Importantly, the data used to generate
FE models is from cadaveric spine specimens that have not
undergone fusion surgery, making predictions about the rate of
degeneration or adjacent-level disease approximations at best.
ese developments highlight the advantages of FEA and
advance the goal of bringing FEA closer to clinical application.
As FE models evolve, the ability to evaluate the spine as a
whole, incorporation of global spinal alignment parameters,
and including elements such as spinal musculature and
ligaments may aid in increasingly accurate predictions of the
spine in vivo. It should also be noted that current FE models
are based on static imaging and do not incorporate dynamic
radiographs (exion, extension, and lateral bending), which
also prove to be important in surgical decision making.
More recently, nonfusion-based spinal implants are being
used as an alternative to stabilizing the spine aer decompres-
sion. Unlike fusion, nonfusion stabilizing systems allow for
angular motion, shear stability, and adjusting to the instant
axis of rotation of the motion segment during movement. Fig.
11.9 shows the L3–S1 spine implanted with a posterior
dynamic stabilizer system (PDS; Disc Motion Technologies).
e implant was placed at L4–L5 following the surgical procedure of total facetectomy at L4–L5. e PDS consisted of a
pair of metallic (chrome-cobalt) sliding parts (male and
female) connected to the spine by titanium pedicle screws at
each side.
To simulate the physiologic loading condition on the spine,
once the implanted model was created, both implanted and
intact models were loaded with 400 N of compressive follower
preload plus 10 Nm of moment to simulate exion, extension,
le/right bending, and le/right rotation. Various biomechanical parameters such as motions, intradiscal pressure, and facet
loads were compared between the intact and implanted model
(Fig. 11.10).
e intervertebral articial disc is another example of
spinal implants recently proposed as a treatment for the
degenerated disc. Unlike fusion systems, the total disc replacement (TDR) promises to address facet pain, mimic the motion
of the intact spine, and avoid degeneration at the adjacent
segment. ere are various designs available for discs. Some
require an anterior surgical approach for replacement as
opposed to others that are placed from the posterior side of
the spine. Fig. 11.11 shows a posterior disc system (Disc
Motion Technologies), including a pair of cobalt-chrome
sliding parts. is disc is placed into the spine following the
surgical removal of the facets at the operative level. Since the
facets are removed, the spine is restabilized by the addition of
a PDS system as previously discussed. e combination of
PDS and disc is a 360-degree motion system that is able to
restore the motion of the operated segment back to normal.
To assess the biomechanics of the implanted spine, FEA was
FIG. 11.10 Fusion system at the L4–L5 level of the lumbar spine.
SECTION
I
PDS system
ROM in flexion
Extensions fixed into
pedicle screws
Ball & socket
joints
FIG. 11.11 The L3–S1 spine implanted with a posterior dynamic stabilizer system at L4–L5. ROM, range of
motion; PDS, posterior dynamic stabilizer.
178 BASIC SCIENCE
used, and motion, intradiscal pressure, and facet loads across
segments were calculated and compared between intact and
implanted models (Figs. 11.10–11.12).
Conclusion
In addition to its most obvious and time-tested uses, such as
the evaluation of early-stage prototypes, FEA is a useful tool
in the evaluation of the biomechanical eect of various surgi-
cal interventions, including a range of implants—from those
that are designed for fusion to motion preservation devices.
FEA aids in predicting the behavior of such implants in the
long term by means of evaluating some crucial mechanical
factors, such as wear and fatigue.
Studies in biomechanics of the spine have shown that FEA
and in vitro cadaveric testing are complementary techniques,
Posterior
artificial disc
FIG. 11.12 The L3–S1 spine implanted with a posterior dynamic stabilizer
and articial disc at L4–L5.
FIG. 11.13 Motion, intradiscal pressure, and facet loads across segments for intact and implanted models.
Ext., extension; Flex., exion; L.B., left bending; L.R., left rotation.
Chapter 11 Finite Element Analysis 179
and thus are well suited to characterize the complex biomechanical behavior of the spine and its anatomic structures,
including internal stresses/strains of the intervertebral disc,
facet joints, and any ligaments of interest. However, like
cadaver investigations, FE models have several limitations. For
example, they do not account for variations in the geometry
of the specimens, such as facet orientation and material properties that vary from specimen to specimen. But, for a given
model geometry, the predicted data are in reasonable agreement with the results from the in vitro investigations. us,
the use of an experimentally validated FE model can provide
very useful information for many clinical questions being
raised by the use of spinal implants.
One of the most far-reaching and interesting questions for
which FEA may be able to provide some insight is in the nature
of adjacent-level degeneration. Because the FE method provides
the means for simulation of changes in motion and loads over
time along with the eects of surgical intervention and changes
in geometry and material properties due to degeneration, highly
advanced, dynamic models of the spine may be able to replicate
the progression of degeneration following surgical intervention
and compare it to the natural course of the disease. While
this will require considerable advancement in FE modeling
techniques, it is perhaps the most promising means of answering
the age-old question of whether adjacent-segment degeneration
is actually attributable to surgical intervention or solely the
manifestation of the underlying disease.
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II
SECTION
DIAGNOSIS
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