Modeling Heat Transfer in Ocular Tissues: Mathematical & Numerical Approaches

[pa-senger]

Student : Pierre-Antoine Senger
Academic supervisors : Christophe Prud’homme, Thomas Saigre and Marcela Szopos
Host institution : Cemosis (IRMA, Université de Strasbourg)
Internship period : Feb 2025 - Aug 2025

Context

This internship took place at Cemosis, the Center for Modeling and Simulation in Stras-
bourg, hosted by the Institute of Advanced Mathematical Research (IRMA). It is part of a
larger effort to develop a digital twin of the human eye, combining advanced mathematical
modeling, numerical simulation, and data assimilation techniques. Within this broader
context, the present work focuses on understanding and simulating the effect of heat
on the human eye during laser treatments. The results obtained during this internship
provide a first step toward integrating optical and thermal processes in a comprehensive
framework for simulating and managing ophthalmological applications.

Methodology

• Tools : PDEs, FEM, Python, C++, Feel++, Monte Carlo, Gaya HPC Cluster, Paraview
• Key steps :
  • Literature review on light–tissue and heat-tissue interaction
  • Mathematical modeling of radiative transfer and heat diffusion
  • Geometry preprocessing and simplification of the eye structure
  • Implementation of Monte Carlo (RTE-MC) and usage of heat solvers in C++/Feel++
  • Coupling optical and thermal models for integrated simulations

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Results

• Implementation of a Monte Carlo solver for radiative transfer in eye tissues
• First coupling with the heat equation to simulate laser-induced heating
• Basis for data assimilation and inverse problem approaches

Validation

Comparison with the results obtained by Arnold and Fichera in Identification of tissue optical properties during thermal laser‐tissue interactions: An ensemble Kalman filter-based approach

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Links

• 📄Internship Report
• 🎤 Presentation slides
• 👔 My CV