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How to Apply: Please refer to the following website for details on how to apply:
http://www.gla.ac.uk/research/opportunities/howtoapplyforaresearchdegree/.
Project Description
Computational modelling of physical and biochemical processes in complex physiological environments has emerged as a means of evaluating current medical device performance with a view to informing future design improvements. The PhD project will focus on cardiovascular applications related to endovascular drug delivery devices (ED’s) for the treatment of obstructive coronary artery disease. At present, patient-specific simulations are only performed retrospectively and usually combine patient-specific arterial geometries with Computational Fluid Dynamics (CFD). These are useful for correlating important haemodynamic indices such as Wall Shear Stress (WSS) and Oscillatory Sher Index (OSI) to patient outcomes. However, patient-specific device design and simulation for decision support is not yet in clinical practice. The primary reason is that the intervention is usually not planned, with the patient arriving in the hospital under emergency conditions. Performing computationally intensive simulations and then manufacturing a patient-specific stent or balloon is therefore not an option. One under-explored aspect of design where personalization holds considerable promise is optimizing the drug dose and release rate. It has recently been shown that the drug level in the artery wall correlates with ED efficacy. It is therefore expected that patient-specific differences in lesion composition and therefore tissue drug transport parameters imply that some patients are currently receiving ineffective or even toxic doses of drug, thereby impacting on the clinical outcomes. Whilst it is impractical to manufacture a full device while a patient is waiting, it is entirely possible to coat a device with a drug. Indeed, the technology already exists to create dose-adjustable stents in the cath-lab. The key scientific barriers to successfully implementing this are (i) making geometry reconstruction from imaging modalities capable of determining lesion composition automatic and (ii) computation time required to solve the resulting system of nonlinear coupled partial differential equations (PDEs) describing fluid flow, drug release and tissue uptake. The goal of the PhD project is to combine state-of-the-art modelling expertise of drug delivery from EDs and imaging-derived geometry reconstruction techniques with novel statistical emulation methods to achieve rapid drug dose optimization.
The critical computational bottleneck for this methodological framework is the numerical integration of the PDEs describing fluid flow, drug release and tissue uptake. This numerical procedure based on finite element (FE) simulations has to be carried out repeatedly as part of an iterative routine aiming to optimize the drug release of the ED. This optimization is critical for patient-specific treatment: too low a drug release rate renders the ED ineffective, whilst too high a rate may be toxic. However, the inclusion of a time-consuming numerical integration step inside an iterative optimization routine leads to excessive computational run times, which makes this approach inviable for any practical clinical application. To deal with this challenging computational complexity and make progress towards a clinical decision support system that can make predictions in real time, the PhD project aims to exploit new opportunities from the fields of Machine Learning and Computational Statistics related to the highly topical field of emulation. The idea is to approximate the computationally expensive mathematical model (the simulator) with a computationally cheap statistical surrogate model (the emulator) by a combination of massive parallelization and nonlinear regression. Starting from a space-filling design in parameter space, the underlying partial differential equations are solved numerically with finite element discretization on a parallel computer cluster, and methods from nonparametric Bayesian statistics based on Gaussian Processes are applied for multivariate smooth interpolation. When new data become available, e.g. in the form of plaque features or flow rates (measured with ultrasound), the resulting proxy objective function can be minimized at low computational costs, without the need for any further computationally expensive FE simulations from the original mathematical model.
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