PhD Position F/M Mathematical models for retinal physiology and pathology [welcome package]

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position


The PhD 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. 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, numerical analysis, scientific computing, data analysis and artificial intelligence.

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


The successful candidate will take part in one or more of the following interdisciplinary research directions:

  • Modelling the biomechanical properties of the cell monolayer of retinal pigment epithelium and their changes due to senescence.
  • Modelling the growth of lesions in the retinal pigment epithelium in presence of age-related macular degeneration.
  • Modelling certain aspects of retinal metabolism related to the renewal of photoreceptor outer segments and the formation of A2E.
  • Refinement and validation of reaction-diffusion models for the biochemistry of the visual cycle.

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




Thresholding scheme and epithelia

  • J. A. Carrillo, H. Murakawa, M. Sato, M. Wang, M. (2024). A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns. bioRxiv, 2024-02.
  • S. Esedoglu. Algorithms for motion of networks by weighted mean curvature. In Proceedings of the International Congress of Mathematicians: Rio de Janeiro 2018, pages 3947–3966. World Scientific, 2018.
  • B. Merriman, J. K. Bence, and S. Osher. Diffusion generated motion by mean curvature. CAM Reports, Department of Mathematics, University of California, Los Angeles, 1992.
  • R. Z. Mohammad, H. Murakawa, K. Svadlenka, and H. Togashi. A numerical algorithm for modeling cellular rearrangements in tissue morphogenesis. Communications Biology, 5(1):239, 2022.

Models for wound healing

  • A. Ravasio, et al. Gap geometry dictates epithelial closure efficiency. Nature communications, 6(1):7683, 2015.
  • L. Bowden, H. Byrne, P. Maini, and D. Moulton. A morphoelastic model for dermal wound closure. Biomechanics and modeling in mechanobiology, 15:663–681, 2016.
  • G. Pozzi and P. Ciarletta. Geometric control by active mechanics of epithelial gap closure. Soft Matter, 20(4), 2024.

Models for the visual cycle

  • L. Alasio, Towards a new mathematical model of the visual cycle. hal-03517553 (2022).
    P. D. Kiser, M. Golczak, and K. Palczewski. Chemistry of the retinoid (visual) cycle. Chemical reviews, 114(1):194–232, 2014.
  • T. D. Lamb, E. N. Pugh Jr. Dark adaptation and the retinoid cycle of vision. Progress in retinal and eye research, 23(3), 307-380, 2004.
  • R. Sharma, C. Schwarz, J. J. Hunter, G. Palczewska, K. Palczewski, D. R. Williams. Formation and clearance of all-trans-retinol in rods investigated in the living primate eye with two-photon ophthalmoscopy. Investigative ophthalmology & visual science, 58(1), 604-613, 2017.

Age-related macular degeneration and medical imaging

  • T. Ach. Age-related macular degeneration, a mathematically tractable disease. Investigative Ophthalmology & Visual Science, 65(3):4–4, 2024.
  • M. Paques, N. Norberg, C. Chaumette, F. Sennlaub, E. Rossi, Y. Borella, and K. Grieve. Long term time-lapse imaging of geographic atrophy: A pilot study. Frontiers in Medicine, 9:868163, 2022.
  • F. Rossant and M. Paques. Normalization of series of fundus images to monitor the geographic atrophy growth in dry age-related macular degeneration. Computer Methods and Programs in Biomedicine, 208:106234, 2021.


Main activities

  • Study previous results, read articles and compile literature reviews.
  • Learn and propose new mathematical methods for theoretical investigation, contribute to experiment design.
  • Learn, develop and test new models and algorithms related to the topic.
  • Conduct numerical simulations, sensitivity analysis and contribute to the model validation based on data.
  • Analyse, criticise and improve both theoretical and applied work.
  • Write scientific articles and reports, often with multiple co-authors.
  • Present new results at conferences and workshops.
  • Write a doctoral thesis.



The candidate must have the following skills:

  • Strong background in applied mathematics, or related fields.
  • Good programming skills, prior experience with FreeFEM, FEniCS, MATLAB or Python is desirable.
  • Proficiency in both written and spoken English.
  • Ability to work independently as well as collaboratively.
  • Ability and desire to read prior work and to build upon it in one’s own work.


Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking
  • Flexible organization of working hours (after 12 months of employment) 
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage


Monthly gross salary : 2100 € during the first and second years. 2190 € the last year.