Percutaneous Coronary Intervention (PCI) is a common clinical procedure used to treat obstructive coronary artery disease, one of the leading causes of death. The overwhelming majority of patients will receive drug-eluting stent devices that act as a supporting scaffold and deliver drugs to counteract renarrowing. While this technology has been truly revolutionary, hundreds of thousands of patients worldwide annually still require an invasive repeat procedure, representing a huge economic burden on society and increasing pressure on health care resources. The key issue is that it is currently not feasible to quantitatively predict the immediate effect of a specific intervention and if/when a patient will suffer from renarrowing in the longer-term. Tools that enable optimisation of the procedure on a patient-specific basis are therefore urgently needed to improve patient outcomes and alleviate the resource burden on healthcare providers. Critical to optimising the procedure is assessment of the individual patient's level of disease. Advances in medical imaging technology now make it possible to visualise the degree of obstruction and, crucially, the composition of the underlying plaque, potentially providing clinicians with a wealth of information to inform and plan PCI. However, decisions are presently left to operator experience and there are no definitive guidelines for how to optimise PCI for a given patient, particularly in complex cases. In recent years, we have seen significant developments in computational models of PCI, that have the potential to inform PCI strategy in the future. However, they suffer from limitations and significant methodological advances are required before they can be routinely integrated within the clinic. These primarily relate to increasing the realism and accuracy of the models, improving their robustness, predictive power and speed of computation. This last point is critical, with the exorbitant run times of current computational models significantly hampering timely decision support and genuine impact in the clinic. The EPSRC Centre for Future PCI Planning will address these challenges by developing a computational decision support tool to assist clinicians with PCI planning. Advances in mathematical modelling of fluid-structure interaction, lesion preparation, drug delivery and growth & remodelling, allied to statistical inference, emulation, uncertainty quantification and optimisation will enable us to create computational tools able to answer key clinical questions like: 1) What will a given patient's artery look like immediately after device deployment? 2) How should the plaque be modified prior to stent deployment, and what specialist tools should be used to do this? 3) What length and diameter of stent should be used, and what should be the balloon deployment inflation pressure? 4) What is the optimal placement of the stent? 5) In the case of complex bifurcation lesions, where potentially multiple stents and balloons are deployed, what is the optimal technique? 6) To what extent is the artery likely to renarrow, over what time course, and how can the PCI strategy be optimised to avoid this? 7) Can we effectively plan PCI solely on pre-procedural imaging such as Computed Tomography? Working together with world-leading International Centres, and a range of leading imaging and medical device companies, the EPSRC Centre for Future PCI Planning will develop novel and robust mathematical and statistical methodologies, supported by large clinical data sets, to create the novel, fast and accurate tools that will help realise our vision of integrating computational tools for PCI planning within the clinic.

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.