Soft tissue related diseases (heart, cancer, eyes) are among the leading causes of death worldwide. Despite extensive biomedical research, a major challenge is a lack of mathematical models that predict soft tissue mechanics across subcellular to whole organ scales during disease progression. Given the tremendous scope, the unmet clinical needs, our limited manpower, and the existence of complementary expertise, we seek to forge NEW collaborations with two world-leading research centres: MIT and POLIMI, to embark on two challenging themes that will significantly stretch the initial SofTMech remit: A) Test-based microscale modelling and upscaling, and B) Beyond static hyperelastic material to include viscoelasticity, nonlinear poroelasticity, tissue damage and healing. Our research will lead to a better understanding of  how our bodies work, and this knowledge will be applied to help medical researchers and clinicians in developing new therapies to minimise the damage caused by disease progression and implants, and to develop more effective treatments. The added value will be a major leap forward in the UK research. It will enable us to model soft tissue damage and healing in many clinical applications, to study the interaction between tissue and implants, and to ensure model reproducibility through in vitro validations. The two underlying themes will provide the key feedback between tissue and cells and ther esponse of cells to dynamic local environments. For example, advanced continuum mechanics approaches will shed newlight on the influence of cell adhesion, angiogenesis and stromal cell-tumour interactions in cancer growth and spread, and on wound healing implant insertion that can be tested with in vitro and in vivo systems. Our theoretical framework will provide insight for the design of new experiments.

Our proposal is unique, timely and cost-effectively because advances in micro- and nanotechnology from MIT and POLIMI now enable measurements of sub-cellular, single cell, and cell-ECM dynamics, so that new theories of soft tissue mechanics at the nano- and micro-scales can be tested using in vitro prototypes purposely built for SofTMech. Bridging the gaps between models at different scales is beyond the ability of any single centre. SofTMech-MP will cluster the criticalmass to develop novel multiscale models that can be experimentally tested by biological experts within the three world-leading Centres. SofTMech-MP will endeavour to unlock the chain of events leading from mechanical factors at subcellular nanoscales to cell and tissue level biological responses in healthy and pathological states by building a new mathematics capacity. Our novel multiscale modelling will lead to new mathematics including new numerical methods, that will be informed and validated by the design and implementation of experiments at the MIT and POLIMI centres. This will be of enormous benefit in attacking problems involving large deformation poroelasticity, nonlinear viscoelasticity, tissue dissection, stent-related tissue damage, and wound healing development. We will construct and analyse data-based models of cellular and sub-cellular mechanics and other responses to dynamic local anisotropic environments, test hypotheses in mechanistic models, and scale these up to tissue-level models (evolutionary equations) for growth and remodelling that will take into account the dynamic, inhomogeneous, and anisotropic movement of the tissue. Our models will be simulated in the various projects by making use of the scientific computing methodologies, including the new computer-intensive methods for learning the parameters of the differential equations directly from noisy measurements of the system, and new methods for assessing alternative structures of the differential equations, corresponding to alternative hypotheses about the underlying biological mechanisms.