There have recently been impressive developments in the mathematical modelling of physiological processes. As part of a previously EPSRC-funded research centre (SofTMech), we have developed mathematical models for the mechanical and electrophysiological processes of the heart, and the flow in the blood vessel network. This allows us to gain deeper insight into the state of a variety of serious cardiovascular diseases, like hypoxia (a condition in which a region of the body is deprived of adequate oxygen supply), angina (reduced blood flow to the heart), pulmonary hypertension (high blood pressure in the lungs) and myocardial infarction (heart attack). A more recent extension of this work to modelling blood flow in the eye also provides novel indicators to assess the degree of traumatic brain injury. What all these models have in common is a complex mathematical description of the physiological processes in terms of differential equations that depend on various material parameters, related e.g. to the stiffness of the blood vessels or the contractility of the muscle fibres. While knowledge of these parameters would be of substantial benefit to the clinical practitioner to help them improve their diagnosis of the disease status, most of the parameters cannot be measured in vivo, i.e. in a living patient. For instance, the determination of the stiffness and contractility of the cardiac tissue would require the extraction of the heart from a patient and its inspection in a laboratory, which can only be done in a post mortem autopsy. It is here that our mathematical models reveal their diagnostic potential. Our equations of the mechanical processes in the heart predict the movement of the heart muscle and how its deformations change in time. These movements can also be observed with magnetic resonance image (MRI) scans, and they depend on the physiological parameters. We can thus compare the predictions from our model with the patterns found in the MRI scans, and search for the parameters that provide the best agreement. In a previous proof-of-concept study we have demonstrated that the physiological parameters identified in this way lead to an improved understanding of the cardiac disease status, which is important for deciding on appropriate treatment options. Unfortunately, the calibration procedure described above faces enormous computational costs. We typically have a large number of physiological parameters, and an exhaustive search in a high-dimensional parameter space is a challenging problem. In addition, every time we change the parameters, our mathematical equations need to be solved again. This requires the application of complex numerical procedures, which take several minutes to converge. The consequence is that even with a high-performance computer, it takes several weeks to determine the physiological parameters in the way described above. It therefore appears that despite their enormous potential, state of the art mathematical modelling techniques can never be practically applied in the clinical practice, where diagnosis and decisions on alternative treatment option have to be made in real time. Addressing this difficulty is the objective of our proposed research. The idea is to approximate the computationally expensive mathematical model by a computationally cheap surrogate model called an emulator. To create this emulator, we cover the parameter space with an appropriate design, solve the mathematical equations in parallel numerically for the chosen parameters, and then fit a non-linear statistical regression model to this training set. After this initial computational investment, the emulator thus created gives predictions for new parameter values practically instantaneously, allowing us to carry out the calibration procedure described above in real time. This will open the doors to harnessing the diagnostic potential of state-of-the art mathematical models for improved decision support in the clinic.

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 the response of cells to dynamic local environments. For example, advanced continuum mechanics approaches will shed new light 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 critical mass 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.

The lifETIME CDT will focus on the development of non-animal technologies (NATs) for use in drug development, toxicology and regenerative medicine. The industrial life sciences sector accounts for 22% of all business R&D spend and generates £64B turnover within the UK with growth expected at 10% pa over the next decade. Analysis from multiple sources [1,2] have highlighted the limitations imposed on the sector by skills shortages, particularly in the engineering and physical sciences area. Our success in attracting pay-in partners to invest in training of the skills to deliver next-generation drug development, toxicology and regenerative medicine (advanced therapeutic medicine product, ATMP) solutions in the form of NATs demonstrates UK need in this growth area. The CDT is timely as it is not just the science that needs to be developed, but the whole NAT ecosystem - science, manufacture, regulation, policy and communication. Thus, the CDT model of producing a connected community of skilled field leaders is required to facilitate UK economic growth in the sector. Our stakeholder partners and industry club have agreed to help us deliver the training needed to achieve our goals. Their willingness, again, demonstrates the need for our graduates in the sector. This CDT's training will address all aspects of priority area 7 - 'Engineering for the Bioeconomy'. Specifically, we will: (1) Deliver training that is developed in collaboration with and is relevant to industry. - We align to the needs of the sector by working with our industrial partners from the biomaterials, cell manufacture, contract research organisation and Pharma sectors. (2) Facilitate multidisciplinary engineering and physical sciences training to enable students to exploit the emerging opportunities. - We build in multidisciplinarity through our supervisor pool who have backgrounds ranging from bioengineering, cell engineering, on-chip technology, physics, electronic engineering, -omic technologies, life sciences, clinical sciences, regenerative medicine and manufacturing; the cohort community will share this multidisciplinarity. Each student will have a physical science, a biomedical science and a stakeholder supervisor, again reinforcing multidisciplinarity. (3) Address key challenges associated with medicines manufacturing. - We will address medicines manufacturing challenges through stakeholder involvement from Pharma and CROs active in drug screening including Astra Zeneca, Charles River Laboratories, Cyprotex, LGC, Nissan Chemical, Reprocell, Sygnature Discovery and Tianjin. (4) Embed creative approaches to product scale-up and process development. - We will embed these approaches through close working with partners including the Centre for Process Innovation, the Cell and Gene Therapy Catapult and industrial partners delivering NATs to the marketplace e.g. Cytochroma, InSphero and OxSyBio. (5) Ensure students develop an understanding of responsible research and innovation (RRI), data issues, health economics, regulatory issues, and user-engagement strategies. - To ensure students develop an understanding of RRI, data issues, economics, regulatory issues and user-engagement strategies we have developed our professional skills training with the Entrepreneur Business School to deliver economics and entrepreneurship, use of TERRAIN for RRI, links to NC3Rs, SNBTS and MHRA to help with regulation training and involvement of the stakeholder partners as a whole to help with user-engagement. The statistics produced by Pharma, UKRI and industry, along with our stakeholder willingness to engage with the CDT provides ample proof of need in the sector for highly skilled graduates. Our training has been tailored to deliver these graduates and build an inclusive, cohesive community with well-developed science, professional and RRI skills. [1] https://goo.gl/qNMTTD [2] https://goo.gl/J9u9eQ