AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting
of the American Society of Biomechanics
Clemson University, South Carolina
September 24-27, 1997
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| AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting |
Computer simulation techniques integrated with engineering mechanics and linkage theory can be used to study the complex in vivo motions and loads of the cervical spine. Validation of computational models of human joints typically uses in vitro biomechanical data obtained from tests on human cadaver tissue. For in vitro studies of cervical spine mechanics, the external motions and loads applied to the end bodies of the specimen are controlled by a testing apparatus. Motions of the interior spinal bodies are measured and are affected by the testing conditions, i.e., mounting and alignment configuration.
Minimal muscle activity is needed to maintain the head in an erect neutral orientation in vivo. When muscles are ignored (as in in-vitro testing), head weight is the typical physiologic force that acts on the cervical spine. During extension of the head from an upright position, a bending moment is induced throughout the spine that increases caudally and acts in combination with the compressive (head weight) force (see Fig. 1). The distribution of the bending moment is affected by the spine's curvature and increases in the caudal direction at each vertebral level with extensional rotation. Based on this analysis, the in vivo characteristics of cervical spine motion and mechanics were: rotations at each vertebral level were continuous with like polarity, combined loading state of axial compression and extensional bending moment, and caudally increasing bending moment distribution.
A computer model of the cervical spine was developed that included the capacity to simulate different mounting configurations. The objective of the study was to compare different biomechanical testing configurations and to identify a mounting arrangement that closely replicated the in vivo extensional motion and loading behavior of the cervical spine. The four simulated experimental set-ups were: upper and lower pots pinned (P-P), upper pot pinned with lower pot fixed (P-F), upper pot connected to a translating, rotating joint offset from a fixed lower pot (TP-F), and upper pot unconstrained and subjected to pure moment with lower pot fixed (M-F).
The simulation software package Working Model 2DTM (Knowledge Revolution, San Mateo, CA) was used to model the cervical spine (C2-T1) and to simulate the four different mounting configurations. The spine was modeled as a mechanically-equivalent system with each vertebral body modeled as a link. The vertebral geometry was approximated as trapezoidal polygons with dimensions taken from anthropometric studies [2]. The mechanical properties of the intervertebral discs were modeled as rotational springs having a linear stiffness value and were located at the center of the subjacent vertebra.
The spine model was initially placed in the TP-F configuration and motion was induced as per a previous experimental protocol [1]. Since the load vector passed closer to the lower pot with increasing spine extension, inverting the spine induced a bending moment that increased in the caudal direction (see Figure 2).
The rotational spring constants were set to the same value and iteratively changed until the loading vector in the simulation correlated to that found in our experimental studies. After successive iterations, a stiffness value of 2.0 N-m/deg for each vertebral level was determined and was comparable to values given in the literature [3].
The model was adapted to simulate the other three mounting configurations. Rotational and moment data at each spinal level and the resultant loading vector were calculated. In all cases except M-F arrangement, motion was initiated by a vertically oriented actuator set to a constant velocity of 3.2 mm/sec. The simulations were stopped when either a force limit (>100 N) or rotation limit (> 30 deg) exceeded the nominal physiologic range. For the M-F case, the simulation was stopped when the bodies reached the maximum rotational limit.
The simulation results of actuator displacement, force in the actuator, total spine rotation, and execution time are listed in Table 1. Figure 3 shows the rotation or moment distribution at each vertebral level. Because the rotation spring constants were linear, the moment values are proportional to the rotation values, i.e. the moment was equal to the vertebral rotation times the spring stiffness.
| End Configuration | ||||
|---|---|---|---|---|
| TP-F | P-F | P-P | M-F | |
| Simulated time (sec) | 32.00 | 0.08 | 0.85 | 0.33 |
| Force at actuator (N) | 49.31 | 109.30 | 102.63 | ------ |
| Actuator travel (mm) | 100.00 | 0.24 | 2.72 | ------ |
| Total rotation (deg) | 30.10 | 0.84 | 7.05 | 11.59 |
Table 1: Computation results for the different end-mounting configurations.
Figure 1: In vivo spine mechanics. Passive head weight induced a caudally increasing moment.
Figure 2: TF-P Simulation at 100mm actuator displacement. The actual loading vector was not in-line with the vertically oriented actuator, but was normal to the connecting arm.
Figure 3: Rotations and moments for the cervical spine simulation at each vertebral level for each of the loading configurations
In the P-F simulation, the upper limit of the actuator force was quickly exceeded. Minimal rotation occurred at each vertebral level and the polarities were negative for levels C2/C3 and C3/C4. A limited range of motion also occurred in the P-P simulation. More important, was the lack of a bending moment at the end vertebral bodies, (i.e., pinned connections can not transfer a moment). For the M-F configuration, the overall spine rotation was less than 12 degrees. Lastly, the TP-F configuration produced physiologic levels of motion (30.10 deg) and load (49.31 N).
1. DiAngelo et al., ASME 1997 Adv in Bioeng, Development of an in vitro experimental protocol to study the extensional mechanics of the cervical spine, (in press).
2. Gilad et al. Brit. J. Rad., 58.695:1031-1034, 1985.
3. Moroney et al., J Biomech., 21.9:769-79, 1988.
