A Mathematical Model to Solve Bio-Heat Transfer Problems through a Bio-Heat Transfer Equation with Quadratic Temperature-Dependent Blood Perfusion under a Constant Spatial Heating on Skin Surface
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Bibliographic record
Abstract
We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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