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 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".