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February 2, 2026ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik7 citations

A dual‐phase‐lag mathematical framework with mechanics‐informed machine learning for predicting ocular thermal risk under environmental heating

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ASAbhinav SinghalRTRakhi TiwariASAbdulkafi Mohammed Saeed

Key Points

  • The central aim is to develop a model that accurately forecasts temperature distributions in the eye during external heating.
  • Created a dual-phase-lag bioheat transfer framework to model thermal behavior in ocular tissues.
  • Applied normal-mode analysis to derive closed-form solutions for six ocular layers.
  • Conducted parametric investigations on factors like temperature, evaporation, porosity, and perfusion.
  • Compared the dual-phase-lag model against existing Lord–Shulman and Fourier models.
  • The dual-phase-lag model significantly outperformed traditional models in predicting realistic thermal responses.
  • Non-Fourier effects were crucial in regulating peak temperatures within ocular tissues.
  • Tissue-level parameters were found to significantly influence intraocular thermal loads.

Abstract

Abstract Thermal damage to ocular tissues is a significant medical issue, as even minor increases in temperature can compromise corneal endothelial function, hasten cataract development, and disturb retinal metabolism. The aim of this study is to create a dependable model for forecasting temperature distributions in the human eye during external heat exposure, thereby facilitating safer therapeutic interventions, refined clinical risk evaluation, and improved environmental health surveillance. A dual‐phase‐lag (DPL) bioheat transfer framework with two relaxation times is created to capture the behavior of thermal waves that travel at a finite speed. Normal‐mode analysis is then used to find closed‐form analytical solutions for all six ocular layers. Parametric investigations measure the effects of things like temperature, evaporation, porosity, and perfusion. When compared to the Lord–Shulman and Fourier models, DPL is clearly better at predicting thermal responses that are realistic for the body. Complementary thermal‐safety mapping, sensitivity analysis, surrogate‐model validation, and response‐surface visualization offer enhanced engineering insights and expedited predictive capabilities. The study reveals that non‐Fourier effects are essential in regulating peak temperatures, and tissue‐level parameters substantially affect intraocular thermal loads. The model's limitations consist of axisymmetric geometry and temperature‐independent material properties, which could be rectified in forthcoming three‐dimensional or patient‐specific investigations. This work offers a medically pertinent and computationally efficient methodology for ocular thermal safety, enhancing healthcare modeling, precision diagnostics, and protective measures for populations subjected to extreme thermal conditions.

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Cite This Study

Singhal et al. (2026) studied this question.

synapsesocial.com/papers/6980fff5c1c9540dea812ea1https://doi.org/10.1002/zamm.70331
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