Post-Doctorant F/H RADIOS - Retinal atrophy: direct & inverse problems & simulations [Action Exploratoire (AEx)]

This project focuses on the study of mathematical models for physiology and pathology of the retina, with a specific interest in degenerative diseases such as Age-related Macular Degeneration (AMD). The overall objective is to develop new mathematical models and techniques, to deepen interdisciplinary knowledge, and to improve simulation algorithms for medical research. The general objective will be approached from different perspectives depending on the specific problem at hand, combining techniques from mathematical analysis, partial differential equations (PDEs), numerical analysis, scientific computing, bio-mechanical modelling, data analysis and artificial intelligence.

The project is intrinsically interdisciplinary and interconnected with Laboratoire Jacques-Louis Lions (UMR 7598), Centre Inria de Paris (équipe MUSCLEES), Hôpital National des Quinze-Vingts (Paris Eye Imaging), Institut de la Vision, Sorbonne Université and Université Paris Cité. The rich research environment offers frequent talks and visits by esteemed researchers, favouring opportunities for collaboration with leading groups in Europe and globally.

The team is working towards a complete simulation pipeline for (dry) AMD progression, from fundus images to simulated atrophy growth and tissue deformation.

Starting date: no later than October 2026.

The successful candidate will take part in a subset of the following interdisciplinary research directions:

• Modelling the bio-mechanical properties of the cell monolayer of Retinal Pigment Epithelium (RPE) and their changes due to senescence by means of microscopic and/or macroscopic models.
• Modelling the growth of lesions in the Retinal Pigment Epithelium in presence of Age-related Macular Degeneration by means of microscopic and/or macroscopic models.
• Bridging across scales: connecting Individual-Based Models for the interactions of epithelial-cell populations structured in size with PDE models at the tissue scale.
• Improving the existing simulation pipeline based on Finite Element Methods for the description of the tissue as a visco-elastic material in 2D or 3D.
• Improving the existing automatic or semi-automatic segmentation algorithms for fundus images of AMD patients and building AI tools to support predictive studies of disease progression.
• Reconstruction of the disease onset: establishing the probable degeneration history before the appearance of AMD lesions with classical and/or AI tools.
• Inference of key bio-mechanical parameters from tissue data with classical and/or AI tools.
• Modelling certain aspects of retinal metabolism related to the renewal of photoreceptor outer segments and the formation of drusen and/or toxic byproducts such as A2E.
• Refinement and validation of reaction-diffusion models for the biochemistry of the visual cycle in rods and cones.

For further details, see the references below or contact L. Alasio (INRIA & LJLL).

References:

1. Curcio CA, Kar D, Owsley C, Sloan KR, Ach T. Age-related macular degeneration, a mathematically tractable disease. Investigative ophthalmology & visual science. 2024.
2. Hernandez RJ, Roberts PA, El-Bouri WK. Advancing treatment of retinal disease through in silico trials. Progress in Biomedical Engineering. 2023.
3. Paques M, Norberg N, Chaumette C, Sennlaub F, Rossi E, Borella Y, Grieve K. Long term time-lapse imaging of geographic atrophy: a pilot study. Frontiers in Medicine. 2022.
4. Rossant F, Paques M. Normalization of series of fundus images to monitor the geographic atrophy growth in dry age-related macular degeneration. Computer Methods and Programs in Biomedicine. 2021.
5. Sala L, Prud'Homme C, Guidoboni G, Szopos M, Harris A. The ocular mathematical virtual simulator: A validated multiscale model for hemodynamics and biomechanics in the human eye. International journal for numerical methods in biomedical engineering. 2024.
6. Doumic M, Hecht S, Hoffmann M, Peurichard D. Scaling limits for a population model with growth, division and cross-diffusion. Mathematical Models and Methods in Applied Sciences. 2025.
7. Gaffney E, Byrne H, Roberts P, Luthert P, Fossbyrne A. Mathematical and computational models of the retina in health, development and disease. Progress in Retinal and Eye Research. 2016.
8. Tlili S, Gay C, Graner F, Marcq P, Molino F, Saramito P. Colloquium: Mechanical formalisms for tissue dynamics. The European Physical Journal E. 2015.
9. Kiser PD, Golczak M, Palczewski K. Chemistry of the retinoid (visual) cycle. Chemical reviews. 2014.
10. Lamb TD, Pugh Jr EN. Dark adaptation and the retinoid cycle of vision. Progress in retinal and eye research. 2004.

• Develop and test new mathematical models, methods and algorithms for tasks such as image segmentation, mesh construction, PDE approximation, scaling limits, model calibration, efficient simulation pipeline.
• Propose new approaches, contribute to experiment design and parameter estimation.
• Conduct numerical simulations, sensitivity analysis and contribute to the model validation.
• Analyse, criticise and improve both theoretical and applied results with classical and/or AI tools.
• Write scientific articles, codes, documentation and reports, often with multiple co-authors.
• Present new results at conferences and workshops.
• Contribute to the activities of équipe MUSCLEES.
• Bibliographic work, interdisciplinary exchange.

The candidate must have the following skills:

• Strong background in PDEs and Mathematical Biology, or related fields.
• Advanced programming skills, prior experience with FreeFEM, FEniCS, MATLAB or Python is expected.
• Proficiency in both written and spoken English, and in scientific communication in general.
• Ability and initiative in building upon previous results and integrating new methods.
• Ability to work independently as well as collaboratively in a multidisciplinary environment, with frequent and constructive interactions with other members of the research group (students, engineers, researchers, clinicians, visitors, etc.).

• Restauration subventionnée
• Transports publics remboursés partiellement
• Congés: 7 semaines de congés annuels + 10 jours de RTT (base temps plein) + possibilité d'autorisations d'absence exceptionnelle (ex : enfants malades, déménagement)
• Possibilité de télétravail et aménagement du temps de travail
• Équipements professionnels à disposition (visioconférence, prêts de matériels informatiques, etc.)
• Prestations sociales, culturelles et sportives (Association de gestion des œuvres sociales d'Inria)
• Mutuelle collective obligatoire (à compter de mai 2026)