On the Modeling of an Intervertebral Disc Using a Novel Large Deformation Multi-Shell Approach
Bibliographic record
Abstract
The objective of this study is to develop an analytical model to predict the stresses and displacements in the lamellae of the intervertebral disc subjected to a compressive force. This is achieved by developing a model based on membrane theory combined to large deformation multishell structural behavior. Equations for longitudinal and circumferential stresses are formulated for each lamella of the anulus fibrosus. Multilamellae interaction is a statically indeterminate problem, which requires equations of compatibility of the displacements of adjacent lamellae to be resolved. The large deformation inherent to soft tissue is considered and the solution is obtained using an iterative process. Elastic interactions with a large deformation is a novelty in analytical modeling of soft tissues. This provides model realism and offers the possibility for new and in-depth investigations. Results are given for longitudinal and circumferential stresses and displacements as well as contact pressures for every lamella of the anulus fibrosus. The analytical results are compared to those of two finite element models. The results suggest that the most highly stressed zone is located on the innermost lamella. Stresses decrease through disc thickness and are at a maximum at the innermost lamella. Circumferential stress is predominant and the difference is less than 5% at any point of the anulus fibrosus when the analytical model is compared to the finite element model using coupled degrees of freedom at the lamellae interface. When compared to the finite element model using contact elements, the difference is below 11%. Contact pressures from the inside to the outside of the anulus fibrosus are shown to decrease nonlinearly. The model presented in this study has demonstrated that it is possible to analytically simulate the complex mechanical behavior of a multishell intervertebral disc subjected to compression, provided some simplifications. Further improvements are suggested to increase model realism and recommendations are given for future experimentation necessary to support both the analytical and numerical models.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".