Our visual perception of the world heavily relies on sophisticated and delicate biological mechanisms, and any disruption to these mechanisms negatively impacts our lives. Age-related macular degeneration (AMD) affects the central field of vision and has become increasingly common in our society, thereby generating a surge of academic and clinical interest. I will present some recent developments in the mathematical modeling of the retinal pigment epithelium (RPE) in the retina in the context of AMD; the RPE cell layer supports photoreceptor survival by providing nutrients and participating in the visual cycle and “cellular maintenance". Our objectives include modeling the aging and degeneration of the RPE with a mechanistic approach, as well as predicting the progression of atrophic lesions in the epithelial tissue. This is a joint work with the research team of Prof. M. Paques at Hôpital National des Quinze-Vingts.

The rheological (deformation and flow) properties of biological tissues  are important in processes such as embryo development, wound healing and 
tumour invasion. Indeed, processes such as these spontaneously generate  stresses within living tissue via active process at the single cell level. 
Tissues are also continually subject to external stresses and deformations  from surrounding tissues and organs. The success of numerous physiological 
functions relies on the ability of cells to withstand stress under some conditions, yet to flow collectively under others. Biological tissue is 
furthermore inherently viscoelastic, with a slow time-dependent mechanics.  Despite this rich phenomenology, the mechanisms that govern the 
transmission of stress within biological tissue, and its response to bulk deformation, remain poorly understood to date.

This talk will describe three recent research projects in modelling the rheology of biological tissue. The first predicts a strain-induced 
stiffening transition in a sheared tissue [1]. The second elucidates the interplay of external deformations applied to a tissue as a whole with 
internal active stresses that arise locally at the cellular level, and shows how this interplay leads to a host of fascinating rheological 
phenomena such as yielding, shear thinning, and continuous or discontinuous shear thickening [2]. The third concerns the formulation of 
a continuum constitutive model that captures several of these linear and nonlinear rheological phenomena [3].

[1] J. Huang, J. O. Cochran, S. M. Fielding, M. C. Marchetti and D. Bi, 
Physical Review Letters 128 (2022) 178001

[2] M. J. Hertaeg, S. M. Fielding and D. Bi, Physical Review X 14 (2024) 
011017.

[3] S. M. Fielding, J. O. Cochran, J. Huang, D. Bi, M. C. Marchetti, 
Physical Review E (Letter) 108 (2023) L042602.

During the talk I will describe my research on host-pathogen interactions during lung infections. Various modelling approaches have been used, including a hybrid multiscale individual-based model that we have developed, which simulates pulmonary infection spread, immune response and treatment within in a section of human lung. The model contains discrete agents which model the spatio-temporal interactions (migration, binding, killing etc.) of the pathogen and immune cells. Cytokine and oxygen dynamics are also included, as well as Pharmacokinetic/Pharmacodynamic models, which are incorporated via PDEs. I will also describe ongoing work to develop a continuum model, comparing the spatial dynamics resulting from these different modelling approaches.  I will focus in the most part on two infectious diseases: Tuberculosis and COVID-19.