Patient-specific blood flow modelling in diagnosis of coronary artery disease

This thesis presents the approach for development of patient-specific coronary blood flow models in 3D and 0D domains based on coronary artery geometries reconstructed from Coronary Computed Tomography Angiography datasets (CCTA). The computed flow patterns extend the diagnostic value of CCTA, which, being noninvasive imaging modality, provides only static information on the anatomy of epicardial arteries. The clinical indices extracted from the virtual blood flow can be potentially employed in the assessment of the haemodynamic severity of Coronary Artery Disease (CAD) lesions as well at the analysis of the underlying mechanisms of formation and localisation of atherosclerotic plaques. However, the existing patient-specific coronary blood flow modelling approaches are generally characterised by relatively high levels of uncertainty and instability due to a number of unknown factors and modelling assumptions. Analysis and comparison of the impact of various modelling assumptions has the potential to reduce this uncertainty. The overarching contributions of this thesis are the thorough analysis and investigation of the existing issues in patient-specific coronary blood flow simulations and the provision of the guidelines for the design and implementation of blood flow models in order to improve and ensure the reliability and accuracy of the numerical results. In addition, a novel approach for the implementation of spatially extended patient-specific 0D blood flow models was proposed, which significantly decreases the high computational costs generally associated with 3D blood flow simulations. While the classical 0D models based on the electrical–hydraulic analogy use the lumped-parameter representation of major vessel tree structures and are thus characterised by limited spatial characteristics, the proposed method for modelling of individual vessel tree branches through a series of 0D elements provides the means for correlation of the computed flow with the precise location along a vessel. Therefore, this extends the applicability of 0D modelling in patient-specific blood flow simulations for the assessment of functional stenosis severity

Patient-specific modelling of the cerebral circulation for aneurysm risk assessment

Cerebral aneurysms are localised pathological dilatations of cerebral arteries, most commonly found in the circle of Willis. Although not all aneurysms are unstable, the major clinical concern involved is the risk of rupture. High morbidity and mortality rates are associated with the haemorrhage resulting from rupture. New indicators of aneurysm stability are sought, since current indicators based on morphological factors have been shown to be unreliable. Haemodynamical factors are known to be relevant in vascular wall remodelling, and therefore believed to play an important role in aneurysmdevelopment and stability. Studies suggest that intra-aneurysmal wall shear stress and flow patterns, for example, are candidate parameters in aneurysm stability assessment. These factors can be estimated if the 3D patient-specific intra-aneurysmal velocity is known, which can be obtained via a combination of in vivo measurements and computational fluid dynamics models. The main determinants of the velocity field are the vascular geometry and flow through this geometry. Over the last decade the extraction of the vascular geometry has become well established. More recently, there has been a shift of attention towards extracting boundary conditions for the 3D vascular segment of interest. The aim of this research is to improve the reliability of the model-based representation of the velocity field in the aneurysmal sac. To this end, a protocol is proposed such that patient-specific boundary conditions for the 3D segment of interest can be estimated without the need for added invasive procedures. This is facilitated by a 1D wave propagation model based on patient-specific geometry and boundary conditions measured non-invasively in more accessible regions. Such a protocol offers improved statistical reliability owing to the increased number of patients that can participate in studies aiming to identify parameters of interest in aneurysm stability assessment. In chapter 2 the intra-aneurysmal velocity field in an idealised aneurysm model is validated with particle image velocimetry experiments, after which the flow patterns are evaluated using a vortex identification method. Chapter 3 describes a 1D model wave propagation model of the cerebral circulation with a patient-specific vascular geometry. The resulting flow pulses at the boundaries of the 3D segment of interest are compared to those obtained with a patient-generic geometry. The influence of these different boundary conditions on the 3D intra-aneurysmal velocity field is evaluated in chapter 4 by prescribing the end-diastolic flows extracted from the 1D models. In order to measure blood flow with videodensitometric methods, an injection of contrast agent is required. The effect of this injection on the flow of interest is assessed in chapter 5. In chapter 6, pressure measurements in the internal carotid are used to evaluate the variability of pressure waveform and its effect on the boundary conditions for the 1D model. Finally, a protocol for full patient-specific modelling is discussed in chapter 7

Numerical modelling of the fluid-structure interaction in complex vascular geometries

A complex network of vessels is responsible for the transportation of blood throughout the body and back to the heart. Fluid mechanics and solid mechanics play a fundamental role in this transport phenomenon and are particularly suited for computer simulations. The latter may contribute to a better comprehension of the physiological processes and mechanisms leading to cardiovascular diseases, which are currently the leading cause of death in the western world. In case these computational models include patient-specific geometries and/or the interaction between the blood flow and the arterial wall, they become challenging to develop and to solve, increasing both the operator time and the computational time. This is especially true when the domain of interest involves vascular pathologies such as a local narrowing (stenosis) or a local dilatation (aneurysm) of the arterial wall. To overcome these issues of high operator times and high computational times when addressing the bio(fluid)mechanics of complex geometries, this PhD thesis focuses on the development of computational strategies which improve the generation and the accuracy of image-based, fluid-structure interaction (FSI) models. First, a robust procedure is introduced for the generation of hexahedral grids, which allows for local grid refinements and automation. Secondly, a straightforward algorithm is developed to obtain the prestress which is implicitly present in the arterial wall of a – by the blood pressure – loaded geometry at the moment of medical image acquisition. Both techniques are validated, applied to relevant cases, and finally integrated into a fluid-structure interaction model of an abdominal mouse aorta, based on in vivo measurements

Tuning of boundary conditions parameters for hemodynamics simulation using patient data

This thesis describes an engineering workflow, which allows specification of boundary conditions and 3D simulation based on clinically available patient-specific data. A review of numerical models used to describe the cardiovascular system is provided, with a particular focus on the clinical target disease chosen for the toolkit, aortic coarctation. Aorta coarctation is the fifth most common congenital heart disease, characterized by a localized stenosis of the descending thoracic aorta. Current diagnosis uses invasive pressure measurement with rare but potential complications. The principal objective of this work was to develop a tool that can be translated into the clinic, requiring minimum operator input and time, capable of returning meaningful results from data typically acquired in clinical practice. Linear and nonlinear 1D modelling approaches are described, tested against full 3D solutions derived for idealized geometries of increasing complexityand for a patient-specific aortic coarctation. The 1D linear implementation is able to represent the fluid dynamic in simple idealized benchmarks with a limited effort in terms of computational time, but in a more complex case, such as a mild aortic coarctation, it is unable to predict well 3D fluid dynamic features. On the other side, the 1D nonlinear implementation showed a good agreement when compared to 3D pressure and flow waveforms, making it suitable to estimate outflow boundary conditions for subject-specific models. A cohort of 11 coarctation patients was initially used for a preliminary analysis using 0D models of increasing complexity to examine parameters derived when tuning models of the peripheral circulation. The first circuit represents the aortic coarctation as a nonlinear resistance, using the Bernoulli pressure drop equation, without considering the effect of downstream circulation. The second circuit include a peripheral resistance and compliance, and separate ascending and descending aortic pressure responses. In the third circuit a supra-aortic Windkessel model was added in order to include the supra-aortic circulation. The analysis detailed represents a first attempt to assess the interaction between local aortic haemodynamics and subject-specific parameterization of windkessel representations of the peripheral and supra-aortic circulation using clinically measured data. From the analysis of these 0D models, it is clear that the significance of the coarctation becomes less from the simple two resistance model to the inclusion of both the peripheral and supra-aortic circulation. These results provide a context within which to interpret outcomes of the tuning process reported for a more complex model of aortic haemodynamics using 1D and 3D model approaches. Earlier developments are combined to enable a multi-scale modelling approach to simulate fluid-dynamics. This includes non-linear 1D models to derive patient-specific parameters for the peripheral and supra-aortic circulation followed by transient analysis of a coupled 3D/0D system to estimate the coarctation pressure augmentation. These predictions are compared with invasively measured catheter data and the influence of uncertainty in measured data on the tuning process is discussed. This study has demonstrated the feasibility of constructing a workflow using non-invasive routinely collected clinical data to predict the pressure gradient in coarctation patients using patient specific CFD simulation, with relatively low levels of user interaction required. The results showed that the model is not suitable for the clinical use at this stage, thus further work is required to enhance the tuning process to improve agreement with measured catheter data. Finally, a preliminary approach for the assessment of change in haemodynamics following coarctation repair, where the coarctation region is enlarged through a virtual intervention process. The CFD approach reported can be expanded to explore the sensitivity of the peak ascending aortic pressure and descending aortic flow to the aortic diameter achieved following intervention, such an analysis would provide guidance for surgical intervention to target the optimal diameter to restore peripheral perfusion and reduce cerebral hypertension

Fluid Flow Simulation and Optimisation with Lattice Boltzmann Methods on High Performance Computers - Application to the Human Respiratory System

An overall strategy for numerical simulations of the full human respiratory system is introduced. The integrative approach takes advantage of numerical simulation, high performance computing and newly developed mathematical optimisation techniques, all based on a mesoscopic model description and on lattice Boltzmann methods as discretisation strategies. Validated numerical results are presented for the simulation of respirations in a real human lung and nose geometry captured by CT

Novel Algorithms for Merging Computational Fluid Dynamics and 4D Flow MRI

Time-resolved three-dimensional spatial encoding combined with three-directional velocity-encoded phase contrast magnetic resonance imaging (termed as 4D flow MRI), can provide valuable information for diagnosis, treatment, and monitoring of vascular diseases. The accuracy of this technique, however, is limited by errors in flow estimation due to acquisition noise as well as systematic errors. Furthermore, available spatial resolution is limited to 1.5mm - 3mm and temporal resolution is limited to 30-40ms. This is often grossly inadequate to resolve flow details in small arteries, such as those in cerebral circulation. Recently, there have been efforts to address the limitations of the spatial and temporal resolution of MR flow imaging through the use of computational fluid dynamics (CFD). While CFD is capable of providing essentially unlimited spatial and temporal resolution, numerical results are very sensitive to errors in estimation of the flow boundary conditions. In this work, we present three novel techniques that combine CFD with 4D flow MRI measurements in order to address the resolution and noise issues. The first technique is a variant of the Kalman Filter state estimator called the Ensemble Kalman Filter (EnKF). In this technique, an ensemble of patient-specific CFD solutions are used to compute filter gains. These gains are then used in a predictor-corrector scheme to not only denoise the data but also increase its temporal and spatial resolution. The second technique is based on proper orthogonal decomposition and ridge regression (POD-rr). The POD method is typically used to generate reduced order models (ROMs) in closed control applications of large degree of freedom systems that result from discretization of governing partial differential equations (PDE). The POD-rr process results in a set of basis functions (vectors), that capture the local space of solutions of the PDE in question. In our application, the basis functions are generated from an ensemble of patient-specific CFD solutions whose boundary conditions are estimated from 4D flow MRI data. The CFD solution that should be most closely representing the actual flow is generated by projecting 4D flow MRI data onto the basis vectors followed by reconstruction in both MRI and CFD resolution. The rr algorithm was used for between resolution mapping. Despite the accuracy of using rr as the mapping step, due to manual adjustment of a coefficient in the algorithm we developed the third algorithm. In this step, the rr algorithm was substituded with a dynamic mode decomposition algorithm to preserve the robustness. These algorithms have been implemented and tested using a numerical model of the flow in a cerebral aneurysm. Solutions at time intervals corresponding to the 4D flow MRI temporal resolution were collected and downsampled to the spatial resolution of the imaging data. A simulated acquisition noise was then added in k-space. Finally, the simulated data affected by noise were used as an input to the merging algorithms. Rigorous comparison to state-of-the-art techniques were conducted to assess the accuracy and performance of the proposed method. The results provided denoised flow fields with less than 1\% overall error for different signal-to-noise ratios. At the end, a small cohort of three patients were corrected and the data were reconstructed using different methods, the wall shear stress (WSS) was calculated using different reconstructed data and the results were compared. As it has been shown in chapter 5, the calculated WSS using different methods results in mutual high and low shear stress regions, however, the exact value and patterns are significantly different

Microfluidics for assessing the behaviour of deformable biological objects

Biological fluids, composed of polymeric solutions or suspensions of deformable particles, commonly present complex rheological behaviour. It is well known that particle-fluid interactions at the microscale dictate the macroscopic flow behaviour of these fluids, however the exact link in numerous situations is still missing. Recently, microfluidic techniques have been widely employed to study the dynamics of microscopic particles under flow.;Even though such techniques present a range of advantages, including the precise control of the flow conditions, as well as the consumption of a small amount of sample, the design of the microfluidic geometries still mostly relies on a trial-and-error approach. In this thesis, we experimentally test a set of microfluidic geometries, the design of which was previously optimised based on theoretical considerations or by means of numerical simulations in order to achieve specific flow conditions.;In addition, we have used complex observation techniques to study the dynamics of solutions and suspensions under flow, identifying microscopic dynamics as well as the major limitations of the microfluidic devices. Biological fluids such as solutions of DNA molecules and red blood cells suspensions were investigated in shear-dominated and extension-dominated flows and the performance of the optimised flow geometries for the study of such biological fluids was demonstrated.Biological fluids, composed of polymeric solutions or suspensions of deformable particles, commonly present complex rheological behaviour. It is well known that particle-fluid interactions at the microscale dictate the macroscopic flow behaviour of these fluids, however the exact link in numerous situations is still missing. Recently, microfluidic techniques have been widely employed to study the dynamics of microscopic particles under flow.;Even though such techniques present a range of advantages, including the precise control of the flow conditions, as well as the consumption of a small amount of sample, the design of the microfluidic geometries still mostly relies on a trial-and-error approach. In this thesis, we experimentally test a set of microfluidic geometries, the design of which was previously optimised based on theoretical considerations or by means of numerical simulations in order to achieve specific flow conditions.;In addition, we have used complex observation techniques to study the dynamics of solutions and suspensions under flow, identifying microscopic dynamics as well as the major limitations of the microfluidic devices. Biological fluids such as solutions of DNA molecules and red blood cells suspensions were investigated in shear-dominated and extension-dominated flows and the performance of the optimised flow geometries for the study of such biological fluids was demonstrated

Numerical Simulation of Particle Deposition in the Human Lungs

We model, simulate and calculate breathing and particle depositions in the human lungs. We review the theory and discretization of fluid mechanics, the anatomy, physiology and measuring methods of lungs. A new model is introduced and investigated with a sensitivity analysis using the singular value decomposition. Particle depositions are simulated in patient-specific and schematized human lungs and compared to the particle deposition in a multiplicative model of subsequent bifurcations