Calculation of Forces in a Lumbar Spine Model with Multiple Support Stays
Bibliographic record
Abstract
McGill (2002) suggested the lumbar spine could be modeled as a mast that was supported by stays composed of the supporting muscles, tendons and ligaments. In his model, the spine is a single member supported by stays attached at the top. Using the Direct Stiffness method (Weaver and Gere, 1990), Hodgdon and Putcha (2006) showed that the force in the supported lumbar spine is reduced by 41.5% using a single set of stays. PURPOSE: The purpose of this research is to expand the previous model by calculating the effect of having multiple stays to anchor the spine. METHODS: The expanded model consists of a set of 5 stacked blocks, simulating the vertebrae of the lumbar spine (L1-L5) with guy wires attached to the each of blocks. For the purposes of this analysis, it is assumed the lumbar spine is divided into 5 equal segments and that the displacements in each of the vertebral blocks are proportional to the distance of each segment from the supporting structure (pelvis). No attempt was made to model the effects of the inter-vertebral disks. The model is treated as a truss in which the rotations are neglected. Thus, the only unknown in this model would be the vertical displacement of the top vertebral block (L1). The displacement is a function of the stiffness of the members. Stiffness is calculated from the length, cross-sectional area and modulus of elasticity. All elements of the model were assumed to have equivalent elastic moduli, and cross-sectional areas. The displacements at the top of other vertebrae (L2-L5) are calculated from displacement of the top vertebrae (L1). Following the calculation of the displacement, the force in the lumbar spine was calculated. RESULTS: When expressed as a function of the force, P applied to the top of the spine, the force on the lumbar spine is determined to be 0.363P. This is equivalent to a reduction of 63.7% in the force in the lumbar spine. CONCLUSION: As one might have assumed, increasing the number of supporting stays reduces the force in the spine model. The addition of 4 pairs of stays reduced the force in the spine model an additional 22.2% beyond that provided by one pair of stays. The addition of guy wire pairs decreases the load in the spine, but they are each less effective than the initial pair of stays.
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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".