Three volunteer subjects provided informed consent and were matched by sex,
age, occupation, and level of cervical disease for comparison of in vivo
dynamics without the need for further stratification. The patient with a fused
cervical spine (anterior cervical discectomy decompression and fusion) and the
patient with a degenerative (spondylotic) cervical spine both had degenerative
disease at the C5-C6 level. The follow-up time after the fusion surgery was
thirty-nine months. In order to recreate bone structures and determine
soft-tissue attachment sites, each subject underwent computed tomography and
magnetic resonance imaging scanning at Vanderbilt University Medical Center
(institutional review board [IRB] #060424). The commercial software Amira
(Mercury Computer Systems, Chelmsford, Massachusetts) was utilized to segment
the computed tomography images. The image processing functions (such as
"threshold," "grow," "shrink,"
"fill," and "smooth") were used to extract the profile
of vertebrae from surrounding soft tissues. The segmented computed tomography
images were used to build the three-dimensional CAD (computer-aided design)
model of each vertebra. Fluoroscopy was used to capture real-time
two-dimensional in vivo motions of the cervical vertebrae in the sagittal
plane while each subject performed an active flexion-extension activity. The
fluoroscopic evaluation allowed for full imaging of C1 through C7 throughout a
subject's entire range of motion. With use of a
three-dimensional-to-two-dimensional registration
method10,
individual fluoroscopic frames were digitized and projected onto an image
plane, and corresponding three-dimensional bone models from computed
tomography images were added to the scene
(Fig. 1). The three-dimensional
in vivo kinematics were then extracted, allowing for the generation of
temporal motion functions for the three-dimensional kinetic analysis.
The three-dimensional mathematical model was derived with use of a set of
differential equations to represent the mechanics of the cervical spine system
during the flexion-extension motion of the neck. The mathematical modeling
technique utilized Kane's method, which is based on an inverse dynamics
approach, utilizing the input of the kinematic data obtained from our computed
tomography and fluoroscopy
model7. This
technique produced the vector sums representing the forces generated by the
muscles, ligaments, and points of contact between intervertebral discs. The
model was simplified with use of a reduction technique that grouped
functionally similar muscles and ligaments together to create a system that
could be solved mathematically. In the three-dimensional mathematical model,
the skull weight (referred to as "SK" in the free-body diagram)
was treated as the only externally applied load during the motion activities
(Fig. 2). The skull and the
cervical spine together were assumed to represent 8.1% of the body
weight10. Each of
the eight osseous elements from C7 to the skull (labeled A, B, C, D, E, H, K,
and S, respectively) was modeled as a rigid body. Specifically, C7 was assumed
to be fixed and hence was treated as the Newtonian reference frame. On each
vertebral body, the origin of the local coordinate system was set up at its
mass center, with the corresponding unit vectors oriented in anteroposterior
and superoinferior directions and referred to as the 1 and 2 directions. Unit
direction 3 (lateral direction) was determined with use of the right-hand
rule. For each vertebra except C7 and C3, two contact points were
defined—one at the superior surface and one at the inferior
surface—whereas only one contact point was defined for C7 (at the
superior surface) and for C3 (at the inferior surface). All contact points
were modeled as moving points from the anterior part to the posterior part
during flexion-extension. At each three-dimensional pose, the
three-dimensional coordinates were automatically calculated by the
mathematical model for each vertebral body. The ligaments evaluated for each
vertebra in this analysis from C3 through C7 were the anterior longitudinal
ligament, posterior longitudinal ligament, interspinous ligament, ligamentum
flavum, and facet capsular ligament. All of the contact points of the
ligaments for the three-dimensional CAD models were digitized from the
corresponding two-dimensional magnetic resonance images based on Yoganandan's
study11 and added
to the mathematical model. The stiffness data for these ligaments were
obtained from Yoganandan's
study11. The
ligamentous forces were calculated according to the displacement between the
two attachment points and the stiffness of the ligaments. The initial length
of each ligament was determined at the neutral position. Then, the deformation
was calculated by subtracting the current length of the deformation of the
ligament from its initial length at each position with respect to time.
Ligaments cannot apply a compressive force, but only a restrictive tensile
force. Thus, if a deformation at any time became smaller than zero, no
ligamentous force was deemed to be applied. An algorithm was designed for this
ligament characteristic and described as the following:
Deformation = Current length — Initial length;If Deformation =0Ligament force = Deformation × StiffnessElse if Deformation <0Ligament force = 0End
Deformation = Current length — Initial length;
If Deformation =0
Ligament force = Deformation × Stiffness
Else if Deformation <0
Ligament force = 0
End
The muscle-switch technique was utilized for the flexor and extensor
muscles in the three-dimensional mathematical model during the
flexion-to-extension motion to simulate the function of the muscles during
motion of the cervical
spine8. The
ligamentous forces, flexor and extensor muscles in three-dimensional space,
and the anteroposterior, compression, and lateral contact forces occurring
from the C3 through C7 levels were calculated directly by the mathematical
model. All of the forces were normalized on the basis of the skull weight of
each patient in order to eliminate differences between patients.
An experimental error analysis was then conducted to verify the results of
the three-dimensional mathematical model by comparing the bearing surface
compression forces as directly measured in a fresh cadaver cervical spine with
the predicted compression forces from the mathematical model. Direct
comparison of the reading from the FlexiForce load/force sensors (Tekscan,
South Boston, Massachusetts) and the predicted compressive forces from our
inverse dynamics mathematical model produced an average error of 5.31%, with a
maximum error of 9.42%.
All three subjects had similar total range of motion of the cervical spine.
The intersegmental rotations of the C1-C2, C2-C3, and C3-C4 levels were not
significantly different among the three subjects. Overall, the subject with
degenerative change at C5-C6 had a relatively smaller range of motion at every
cervical level except at C4-C5. For the patient with anterior cervical
discectomy decompression and fusion, abnormally increased ranges of motion (up
to 6.3° or 36% more flexion-extension at the superior [C4-C5] level and up
to 7.6° or 52.5% more flexion-extension at the inferior [C6-C7] level)
were observed at the adjacent levels when compared with the data from the
normal subject. In all three patients, the magnitudes of the coupled lateral
bending and axial rotation between vertebral bodies during flexion-extension
were all less than 1°, except those at C6-C7 for the subject with anterior
cervical discectomy decompression and fusion, who had 1.9° of coupled
lateral bending rotation (8.60% of flexion-extension rotation) and 7.9° of
coupled axial rotation (35.75% of flexion-extension rotation), with 22.1°
of flexion-extension rotation.
The anteroposterior and compression force patterns among the three subjects
were derived from the three-dimensional mathematical model, and their plots
are shown in Figure 3. With use
of the three-dimensional mathematical model, the anteroposterior, compression,
and lateral forces and the force patterns were calculated at segments adjacent
(C4-C5, C6-C7) to the symptomatic level (C5-C6) and also at the next
sequential segment (C3-C4). At the C4-C5 level, average anteroposterior forces
(direction 1 in Fig. 2) were
0.28 times skull weight (SW) (range, 0 to 0.47 SW) in the normal subject; 0.14
SW (range, —0.19 to 0.35 SW) in the subject with degenerative changes at
C5-C6; and 0.45 SW (range, —1.81 to 0.51 SW) in the subject with a
fusion at C5-C6. The average anteroposterior forces at the C6-C7 level were
0.29 SW (range, —0.02 to 0.64 SW) in the normal subject; 0.26 SW (range,
—1.09 to 0.37 SW) in the subject with degenerative changes; and
—0.53 SW (range, —2.69 to 0.52 SW) in the patient with a fusion.
At the C3-C4 level, there was no significant difference between the normal
subject and the subject with a fusion, as average values were 0.26 SW (range,
0 to 0.46 SW) in the normal subject and 0.13 SW (range, 0.02 to 0.46 SW) in
the subject with a fusion; but the subject with degenerative changes had a
smaller average value of 0.12 SW (range, —0.46 to 0.26 SW) and a smaller
maximum value of 0.26 SW.
In the normal subject, the average compression forces (direction 2 in
Fig. 2) at the C4-C5 and C6-C7
levels were 1.32 SW and 1.74 SW (range, 0.79 to 1.68 SW and 0.93 to 2.83 SW),
respectively. The patient with degenerative changes at C5-C6 exhibited average
compression forces of 1.27 SW (range, 0.79 to 1.58 SW) at the C4-C5 level and
1.59 SW (range, 0.93 to 2.10 SW) at the C6-C7 level. The average compression
force values for the patient with a fusion at C5-C6 were 1.80 SW (range, 0.81
to 2.91 SW) and 2.21 SW (range, 0.98 to 4.78 SW), respectively. At the C3-C4
level, there was no significant difference among these three subjects, as the
normal subject had an average compression force value of 1.24 SW (range, 0.72
to 1.56 SW), the patient with degenerative changes had a value of 1.15 SW
(range, 0.71 to 1.51 SW), and the subject with a fusion at C5-C6 had a value
of 1.08 SW (range, 0.71 to 1.44 SW).
The lateral forces (direction 3 in Fig.
2) for all three subjects were small. At the C4-C5 and C6-C7
levels, the average values were 0.06 SW (range, —0.13 to 0.08 SW) and
0.07 SW (range, —0.05 to 0.15 SW) in the normal subject, 0.16 SW (range,
0 to 0.33 SW) and 0.17 SW (range, 0 to 0.33 SW) in the patient with
degenerative changes, and —0.07 SW (range, —0.16 to 0.04 SW) and
0.04 SW (range, —0.10 to 0.07 SW) in the patient with a fusion,
respectively. At the C3-C4 level, the average forces were 0.07 SW (range, 0 to
0.09 SW) in the normal subject, 0.15 SW (range, 0 to 0.33 SW) in the patient
with degenerative changes, and 0.08 SW (range, 0 to 0.21 SW) in the patient
with a fusion.