Observing and Describing the Sigmoidal Growth of Bone Anchorage from Endosseous Healing with Empirical Models
Bibliographic record
Abstract
The concept of endosseous healing creating a secondary biologic stability is firmly established in the dental literature, but mathematical growth curves have not been used to describe the resultant increase in bone anchorage (BA). This work investigates the hypothesis that the effect of implant surface topography on BA can be quantified using the appropriate empirical model and that increases in BA follow a sigmoidal growth curve with features that are consistent with the three general phases of endosseous healing: the lag phase with osteoconduction, the growth phase with de novo bone formation, and the plateau phase with remodeling. BA of rectangular implants placed in rat femora were tested in both shear and tension. Initial anchorage measurements taken at 5-days occurred after the lag phase, but growth and plateau phases were apparent in the data and could be measured using the asymptotic model. Testing method was found to significantly affect the peak BA and the inclusion of nanotopography on a microtopographically complex surface significantly decreased the required healing time. The effect of nanotopography was found to be greater than the effect of surface chemistry or hydrophilicity. Cylindrical and threaded implants were tested in torsion after being placed in rat tibiae for up to 6 months. By taking BA measurements at 3-days after placement the lag phase could be observed, enabling the fitting of sigmoidal functions with the logistic function producing the best fit. This allowed for the description of the peak anchorage, inflection point, and healing time. By differentiating between the phases of endosseous healing it was found that implant topography had a significant effect on de novo bone formation but not remodeling. This work has shown the three phases of increasing BA, related the increase of BA to bone formation, and found that curve fitting is an effective means of comparing different implant designs with respect to BA achieved through endosseous healing.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".