A Mathematical Model for Predicting Ultrasonic Measurement of Total Knee Replacement Contact Areas
Bibliographic record
Abstract
A simple mathematical model was developed to characterize diagnostic ultrasound behavior at two-body interfaces of known geometry. The model was based on a 2-D curved-on-flat geometry comprising an infinitely long circular cylinder indenting a flat infinite half-space creating a known contact width W(0). The effects of indenter radius R(F) ultrasound resonance wavelength lambda/2, and ultrasound beam thickness BT on the size of the predicted interfacial contact width W(1) were investigated. Since the model was purely geometric in nature, material properties of the mating bodies were not considered. A theoretical sensitivity analysis was performed on the model using geometries representative of commercially available orthopedic total knee replacements (TKRs) and typical diagnostic ultrasound resolutions. This investigation was part of an ongoing project to develop an engineering design tool for measuring surface contact areas at the tibio-femoral interfaces of clinically employed TKR prostheses.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.002 | 0.001 |
| 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".