Efficient numerical modelling of time-domain light propagation in curved 3D absorbing and scattering media with finite differences
Bibliographic record
Abstract
biological tissues) with curved boundaries. It relies on the finite difference method (FDM) in conjuction with the Crank-Nicolson method for accurately solving the optical diffusion equation (DE). The strength of the FDM lies in its simplicity and efficiency, since the equations are easy to set up, and accessing neighboring grid points only requires simple memory operations, leading to efficient code execution. Owing to its use of Cartesian grids, the FDM is generally thought cumbersome compared to the finite element method (FEM) for dealing with media with curved boundaries. However, to apply the FDM to such media, the blocking-off method can be resorted to. To account for the change of the refractive index at the boundary, Robin-type boundary conditions are considered. This requires the computation of surface normals. We resort here for the first time to the Sobel operator borrowed from image processing to perform this task. The Sobel operator is easy to implement, fast, and allows obtaining a smooth field of normal vectors along the boundary. The main contribution of this work is to arrive at a complete numerical FDM-based model of light propagation in the time domain in 3D absorbing and scattering media with curved geometries, taking into account realistic refractive index mismatch boundary conditions. The fluence rate obtained with this numerical model is shown to reproduce well that obtained with independent gold-standard Monte Carlo simulations.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".