The mechanical properties of biological tissues are important in processes such as embryo development, wound healing and tumour invasion. 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 start with a pedagogical introduction to the general research area of soft condensed matter physics, with a particular focus on rheology (the study of deformation and flow); followed by a pedagogical introduction to the topic of amorphous soft matter, and the basic philosophy of modelling biological issue as an example of active amorphous soft matter.
Time permitting, three recent research projects in modelling the rheology of biological tissue will then be outlined. 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.