Analytical Solutions for the Cardiac Extracellular‐Membrane‐Intracellular Model
Bibliographic record
Abstract
ABSTRACT The cardiac extracellular‐membrane‐intracellular (EMI) model is a novel mathematical framework for cardiac electrophysiology simulations. The cardiac EMI model provides a more detailed description of the heart's electrical activity compared to traditional monodomain and bidomain models, potentially making it better‐suited for understanding the electrical dynamics of the heart under pathological conditions. In this paper, we derive and verify several analytical solutions for the cardiac EMI model. Specifically, we obtain a family of solutions for a single two‐dimensional cell in polar coordinates and for a pair of coupled three‐dimensional cells in spherical coordinates. To verify the analytical solutions, we conduct numerical experiments using the mortar finite element method combined with operator splitting. The results demonstrate that these analytical solutions are effective for verifying the accuracy of software that performs numerical simulations of the cardiac EMI model.
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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 | 0.008 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| 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".