Partitioning of Arterial Tree for Parallel Decomposition of Hemodynamic Calculations

AbstractModeling of fluid mechanics for the vascular system is of great value as a source of knowledge about development, progression, and treatment of cardiovascular disease. Full three-dimensional simulation of blood flow in the whole human body is a hard computational problem. We discuss parallel decomposition of blood flow simulation as a graph partitioning problem. The detailed model of full human arterial tree and some simpler geometries are discussed. The effectiveness of coarse-graining as well as pure spectral approaches is studied. Published data can be useful for development of parallel hemodynamic applications as well as for estimation of their effectiveness and scalability

Flexible multivariate hemodynamics fMRI data analyses and simulations with PyHRF

International audienceAs part of fMRI data analysis, the pyhrf package provides a set of tools for addressing the two 3 main issues involved in intra-subject fMRI data analysis: (i) the localization of cerebral regions 4 that elicit evoked activity and (ii) the estimation of the activation dynamics also referenced to 5 as the recovery of the Hemodynamic Response Function (HRF). To tackle these two problems, 6 pyhrf implements the Joint Detection-Estimation framework (JDE) which recovers parcel-level 7 HRFs and embeds an adaptive spatio-temporal regularization scheme of activation maps. With 8 respect to the sole detection issue (i), the classical voxelwise GLM procedure is also available 9 through nipy, whereas Finite Impulse Response (FIR) and temporally regularized FIR models 10 are implemented to deal with HRF estimation concerns (ii). Several parcellation tools are also 11 integrated such as spatial and functional clustering. Parcellations may be used for spatial 12 averaging prior to FIR/RFIR analysis or to specify the spatial support of the HRF estimates 13 in the JDE approach. These analysis procedures can be applied either to volumic data sets or 14 to data projected onto the cortical surface. For validation purpose, this package is shipped with 15 artificial and real fMRI data sets, which are used in this paper to compare the outcome of the 16 different available approaches. The artificial fMRI data generator is also described to illustrate 17 how to simulate different activation configurations, HRF shapes or nuisance components. To 18 cope with the high computational needs for inference, pyhrf handles distributing computing 19 by exploiting cluster units as well as multiple cores computers. Finally, a dedicated viewer is 20 presented, which handles n-dimensional images and provides suitable features to explore whole 21 brain hemodynamics (time series, maps, ROI mask overlay)

Lattice-Boltzmann simulations of cerebral blood flow

Computational haemodynamics play a central role in the understanding of blood behaviour in the cerebral vasculature, increasing our knowledge in the onset of vascular diseases and their progression, improving diagnosis and ultimately providing better patient prognosis. Computer simulations hold the potential of accurately characterising motion of blood and its interaction with the vessel wall, providing the capability to assess surgical treatments with no danger to the patient. These aspects considerably contribute to better understand of blood circulation processes as well as to augment pre-treatment planning. Existing software environments for treatment planning consist of several stages, each requiring significant user interaction and processing time, significantly limiting their use in clinical scenarios. The aim of this PhD is to provide clinicians and researchers with a tool to aid in the understanding of human cerebral haemodynamics. This tool employs a high performance fluid solver based on the lattice-Boltzmann method (coined HemeLB), high performance distributed computing and grid computing, and various advanced software applications useful to efficiently set up and run patient-specific simulations. A graphical tool is used to segment the vasculature from patient-specific CT or MR data and configure boundary conditions with ease, creating models of the vasculature in real time. Blood flow visualisation is done in real time using in situ rendering techniques implemented within the parallel fluid solver and aided by steering capabilities; these programming strategies allows the clinician to interactively display the simulation results on a local workstation. A separate software application is used to numerically compare simulation results carried out at different spatial resolutions, providing a strategy to approach numerical validation. This developed software and supporting computational infrastructure was used to study various patient-specific intracranial aneurysms with the collaborating interventionalists at the National Hospital for Neurology and Neuroscience (London), using three-dimensional rotational angiography data to define the patient-specific vasculature. Blood flow motion was depicted in detail by the visualisation capabilities, clearly showing vortex fluid ow features and stress distribution at the inner surface of the aneurysms and their surrounding vasculature. These investigations permitted the clinicians to rapidly assess the risk associated with the growth and rupture of each aneurysm. The ultimate goal of this work is to aid clinical practice with an efficient easy-to-use toolkit for real-time decision support

Modeling Cardiovascular Hemodynamics Using the Lattice Boltzmann Method on Massively Parallel Supercomputers

Accurate and reliable modeling of cardiovascular hemodynamics has the potential to improve understanding of the localization and progression of heart diseases, which are currently the most common cause of death in Western countries. However, building a detailed, realistic model of human blood flow is a formidable mathematical and computational challenge. The simulation must combine the motion of the fluid, the intricate geometry of the blood vessels, continual changes in flow and pressure driven by the heartbeat, and the behavior of suspended bodies such as red blood cells. Such simulations can provide insight into factors like endothelial shear stress that act as triggers for the complex biomechanical events that can lead to atherosclerotic pathologies. Currently, it is not possible to measure endothelial shear stress in vivo, making these simulations a crucial component to understanding and potentially predicting the progression of cardiovascular disease. In this thesis, an approach for efficiently modeling the fluid movement coupled to the cell dynamics in real-patient geometries while accounting for the additional force from the expansion and contraction of the heart will be presented and examined. First, a novel method to couple a mesoscopic lattice Boltzmann fluid model to the microscopic molecular dynamics model of cell movement is elucidated. A treatment of red blood cells as extended structures, a method to handle highly irregular geometries through topology driven graph partitioning, and an efficient molecular dynamics load balancing scheme are introduced. These result in a large-scale simulation of the cardiovascular system, with a realistic description of the complex human arterial geometry, from centimeters down to the spatial resolution of red-blood cells. The computational methods developed to enable scaling of the application to 294,912 processors are discussed, thus empowering the simulation of a full heartbeat. Second, further extensions to enable the modeling of fluids in vessels with smaller diameters and a method for introducing the deformational forces exerted on the arterial flows from the movement of the heart by borrowing concepts from cosmodynamics are presented. These additional forces have a great impact on the endothelial shear stress. Third, the fluid model is extended to not only recover Navier-Stokes hydrodynamics, but also a wider range of Knudsen numbers, which is especially important in micro- and nano-scale flows. The tradeoffs of many optimizations methods such as the use of deep halo level ghost cells that, alongside hybrid programming models, reduce the impact of such higher-order models and enable efficient modeling of extreme regimes of computational fluid dynamics are discussed. Fourth, the extension of these models to other research questions like clogging in microfluidic devices and determining the severity of co-arctation of the aorta is presented. Through this work, a validation of these methods by taking real patient data and the measured pressure value before the narrowing of the aorta and predicting the pressure drop across the co-arctation is shown. Comparison with the measured pressure drop in vivo highlights the accuracy and potential impact of such patient specific simulations. Finally, a method to enable the simulation of longer trajectories in time by discretizing both spatially and temporally is presented. In this method, a serial coarse iterator is used to initialize data at discrete time steps for a fine model that runs in parallel. This coarse solver is based on a larger time step and typically a coarser discretization in space. Iterative refinement enables the compute-intensive fine iterator to be modeled with temporal parallelization. The algorithm consists of a series of prediction-corrector iterations completing when the results have converged within a certain tolerance. Combined, these developments allow large fluid models to be simulated for longer time durations than previously possible.Engineering and Applied Science

Image-Based Quantification Workflow for Coronary Morphology: A Tool for Use in Next-Generation Bifurcation Stent Design

Coronary artery disease (CAD) occurs in ~200,000 bifurcation lesions annually. Treatment of CAD near bends and bifurcations is challenging and a preferred strategy for bifurcation lesions has yet to be established. However, a favorable treatment option may be elucidated by a more thorough understanding of vessel morphology as well as local hemodynamic alterations caused by current stenting approaches. Computational modeling of human arteries offers an attractive way to investigate the relationships between geometry, hemodynamics and vascular disease. Recent developments also make it possible to perform analysis on realistic geometries acquired noninvasively. The objective of this work was twofold. The first aim was to build on previous work in this area by quantifying hemodynamic alterations introduced by treatment of an idealized coronary bifurcation using several approaches that involve multiple stents. Each model was created using combined computer aided design techniques and computational fluid dynamics (CFD) analysis tools. Resting and hyperemic blood flow conditions were also studied to determine the severity of local hemodynamic alterations and for comparison to previous results. Indices of time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) were quantified for four idealized computational models. The luminal surface exposed to low TAWSS was similar in the main vessel (MV) for all models. Greatest differences were noted between un-stented versus stented side branch vessels (ex. rest: 1% vs. 35%). Sites of elevated OSI (\u3e0.1) were minimal, except under hyperemia conditions in the MV (10% surface area). Flow disturbances were quantified for each provisional technique used, illustrating how stents protruding in main vessels impact flow profiles. Stents without kissing balloon dilation had abnormal flow disturbances, but showed decreased percentage of area exposed to areas of low WSS. A second aim of this work was to design a robust and unbiased method to quantify vessel morphology and representative trends for three bifurcation sites prone to CAD. Computational models of these sites were generated using computed topography images from 22 patients. Models were used to query geometric characteristics from each bifurcation site including area, length, eccentricity, taper, curvature and bifurcation angles. Post-processing was accomplished by a combination of statistical methods and clustering analysis. Vessel length and area were significantly different within and between bifurcation sites. The left main coronary artery (LCA) bifurcation was significantly different from its two daughter bifurcations (left anterior descending and left circumflex arteries). Specifically vessel area and length were significantly different both between and within bifurcation sites. The daughter bifurcation sites were similar for all characteristics. Vessel area and length proved to be the most useful properties for identifying trends within a particular bifurcation site. The outcome of this work provides a workflow for characterizing coronary bifurcations and a strong foundation for elucidating common parameters from normal, healthy coronary arteries. Collectively these results from idealized and patient-specific coronary bifurcations offer additional insight into the impact of current treatment approaches and characteristics associated with current stenting techniques. Flow disturbances and local hemodynamic changes have been quantified for provisional techniques currently used. These methods and results may ultimately be useful in the design of next-generation bifurcation stents

Fluid-Structure Interaction Problems in Hemodynamics:Parallel Solvers, Preconditioners, and Applications

In this work we aim at the description, study and numerical investigation of the fluid-structure interaction (FSI) problem applied to hemodynamics. The FSI model considered consists of the Navier-Stokes equations on moving domains modeling blood as a viscous incompressible fluid and the elasticity equation modeling the arterial wall. The fluid equations are derived in an arbitrary Lagrangian-Eulerian (ALE) frame of reference. Several existing formulations and discretizations are discussed, providing a state of the art on the subject. The main new contributions and advancements consist of: A description of the Newton method for FSI-ALE, with details on the implementation of the shape derivatives block assembling, considerations about parallel performance, the analytic derivation of the derivative terms for different formulations (conservative or not) and for different types of boundary conditions. The implementation and analysis of a new category of preconditioners for FSI (applicable also to more general coupled problems). The framework set up is general and extensible. The proposed preconditioners allow, in particular, a separate treatment of each field, using a different preconditioning strategy in each case. An estimate for the condition number of the preconditioned system is proposed, showing how preconditioners of this type depend on the coupling, and explaining the good performance they exhibit when increasing the number of processors. The improvement of the free (distributed under LGPL licence) parallel finite elements library LifeV. Most of the methods described have been implemented within this library during the period of this PhD and all the numerical tests reported were run using this framework. The simulation of clinical cases with patient-specific data and geometry, the comparison on simulations of physiological interest between different models (rigid, FSI, 1D), discretizations and methods to solve the nonlinear system. A methodology to obtain patient-specific FSI simulations starting from the raw medical data and using a set of free software tools is described. This pipeline from imaging to simulation can help medical doctors in diagnosis and decision making, and in understanding the implication of indicators such as the wall shear stress in the pathogenesis

Bayesian learning of continuous time dynamical systems with applications in functional magnetic resonance imaging

Temporal phenomena in a range of disciplines are more naturally modelled in continuous-time than coerced into a discrete-time formulation. Differential systems form the mainstay of such modelling, in fields from physics to economics, geoscience to neuroscience. While powerful, these are fundamentally limited by their determinism. For the purposes of probabilistic inference, their extension to stochastic differential equations permits a continuous injection of noise and uncertainty into the system, the model, and its observation. This thesis considers Bayesian filtering for state and parameter estimation in general non-linear, non-Gaussian systems using these stochastic differential models. It identifies a number of challenges in this setting over and above those of discrete time, most notably the absence of a closed form transition density. These are addressed via a synergy of diverse work in numerical integration, particle filtering and high performance distributed computing, engineering novel solutions for this class of model. In an area where the default solution is linear discretisation, the first major contribution is the introduction of higher-order numerical schemes, particularly stochastic Runge-Kutta, for more efficient simulation of the system dynamics. Improved runtime performance is demonstrated on a number of problems, and compatibility of these integrators with conventional particle filtering and smoothing schemes discussed. Finding compatibility for the smoothing problem most lacking, the major theoretical contribution of the work is the introduction of two novel particle methods, the kernel forward-backward and kernel two-filter smoothers. By harnessing kernel density approximations in an importance sampling framework, these attain cancellation of the intractable transition density, ensuring applicability in continuous time. The use of kernel estimators is particularly amenable to parallelisation, and provides broader support for smooth densities than a sample-based representation alone, helping alleviate the well known issue of degeneracy in particle smoothers. Implementation of the methods for large-scale problems on high performance computing architectures is provided. Achieving improved temporal and spatial complexity, highly favourable runtime comparisons against conventional techniques are presented. Finally, attention turns to real world problems in the domain of Functional Magnetic Resonance Imaging (fMRI), first constructing a biologically motivated stochastic differential model of the neural and hemodynamic activity underlying the observed signal in fMRI. This model and the methodological advances of the work culminate in application to the deconvolution and effective connectivity problems in this domain