The Mathematical Model of a Procedure for Percutaneous Annuloplasty
Bibliographic record
Abstract
Existing mathematical models of the mitral valve allow the simulation of ring open-heart annuloplasty procedures intended to reduce the lumen of the valve. Using these models, only a posteriori effects can be predicted. With the advent of novel percutaneous annuloplasty approaches, there is a need to describe a priori effects; in particular, this paper focuses on a technique which consists of sequentially installing interconnected anchors around the mitral annulus, whose lumen is reduced by the tightening of the tethered wire. We develop here a static mathematical model of the mitral annulus that takes into account the mechanical response of its tissue and the surrounding muscular tissue. A number of roughly coplanar points corresponding to anchor positions, at about equal distantes, are identified on the annulus. Each of these points is then attached to a linearly elastic spring of a given stiffness, The spring-end is connected to a fixed pinned support, the other end supporting the wire, that forms a loop. With this model we estimate the anchor-points position vectors after lumen reduction and the wire tension that is needed to reduce the perimeter of the polygon defined by the anchor points to a given value, which, for each patient, is related to the desired lumen. This formulation leads to the minimization of the potential energy of the mechanical system over the position vectors of the anchor points after tightening, which are the design variables. These are found by solving the first-order normality conditions of the equality-constrained optimization problem. Preliminary experimental data obtained on cadaveric swine hearts validate the model: it can be used to predict, for a given perimeter size reduction, the wire tension as well as the anchor position after repair.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
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".