A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models
Bibliographic record
Abstract
PURPOSE: The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model. METHOD: The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation. RESULTS: The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress. CONCLUSION: Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".