Do Alterations in Vertebral and Disc Dimensions Affect an Elliptical Model of Thoracic Kyphosis?
Bibliographic record
Abstract
STUDY DESIGN: Mathematical modeling, using least squares method, of thoracic kyphosis was constructed as digitized points from radiographs of 50 healthy patients. OBJECTIVE: To determine a simple geometric model of the thoracic kyphosis. SUMMARY OF BACKGROUND DATA: Thoracic kyphosis is an important parameter of health, but geometric models of kyphosis are rare. Few papers report vertebral body and disc height data. METHODS: Thoracic vertebral bodies were digitized on lateral radiographs of 50 healthy patients. The average path of the posterior vertebral body corners of T1 through T12 was modeled, in the least squares sense, with a portion of an ellipse. The best-fit ellipse was sectioned with different model partitions using four sets of vertebral body heights and disc heights. Segmental and global angles derived from these four models were compared with reported values in the literature. RESULTS: A 72 degrees portion of an ellipse, with a minor-to-major axis ratio of 0.69, can closely approximate the path of the posterior body corners from the inferior of T1 to the superior of T12. The posterior vertebral body heights and disc heights have an average ratio of approximately 5:1. Segmental angles from T3-T4 through T11-T12 for all four models are close to other reported values. The thoracic spine has a height-to-length ratio of approximately 0.96. CONCLUSIONS: Thoracic kyphosis from inferior-posterior T1 to superior-posterior T12 can be closely modeled (least squares error per point < 1 mm) with a 72 degrees piece of an ellipse with a minor-to-major axis ratio of 0.69. The major axis is parallel to the posterior body margin of T12, whereas the minor axis passes through the superior endplate of T12. Segmental angles derived from this elliptical modeling are in the range of values from healthy patients.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".