Theoretical limitations of the elastic wave equation inversion for tissue elastography
Bibliographic record
Abstract
This article examines the theoretical limitations of the local inversion techniques for the measurement of the tissue elasticity. Most of these techniques are based on the estimation of the phase speed or the algebraic inversion of a one-dimensional wave equation. To analyze these techniques, the wave equation in an elastic continuum is revisited. It is proven that in an infinite medium, harmonic shear waves can travel at any phase speed greater than the classically known shear wave speed, mu/rho, by demonstrating this for a special case with cylindrical symmetry. Hence in addition to the mechanical properties of the tissue, the phase speed depends on the geometry of the wave as well. The elastic waves in an infinite cylindrical rod are studied. It is proven that multiple phase speeds can coexist for a harmonic wave at a single frequency. This shows that the phase speed depends not only on the mechanical properties of the tissue but also on its shape. The final conclusion is that the only way to avoid theoretical artifacts in the elastograms obtained by the local inversion techniques is to use the shear wave equation as expressed in the curl of the displacements, i.e., the rotations, for the inversion.
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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 | 0.014 | 0.061 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".