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Alnaes M.S.,Center for Biomedical Computing | Logg A.,Center for Biomedical Computing | Olgaard K.B.,University of Aalborg | Rognes M.E.,Center for Biomedical Computing | Wells G.N.,University of Cambridge
ACM Transactions on Mathematical Software | Year: 2014

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Mortensen M.,University of Oslo | Mortensen M.,Center for Biomedical Computing | Valen-Sendstad K.,Center for Biomedical Computing | Valen-Sendstad K.,King's College
Computer Physics Communications | Year: 2015

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework. © 2014 Elsevier B.V.

Valen-Sendstad K.,University of Toronto | Valen-Sendstad K.,Center for Biomedical Computing | Steinman D.A.,University of Toronto
American Journal of Neuroradiology | Year: 2014

BACKGROUND AND PURPOSE: Computational fluid dynamics has become a popular tool for studying intracranial aneurysm hemodynamics, demonstrating success for retrospectively discriminating rupture status; however, recent highly refined simulations suggest potential deficiencies in solution strategies normally used in the aneurysm computational fluid dynamics literature. The purpose of the present study was to determine the impact of this gap. MATERIALS AND METHODS: Pulsatile flow in 12 realistic MCA aneurysms was simulated by using both high-resolution and normal-resolution strategies. Velocity fields were compared at selected instants via domain-averaged error. We also compared wall shear stress fields and various reduced hemodynamic indices: cycle-averaged mean and maximum wall shear stress, oscillatory shear index, low shear area, viscous dissipation ratio, and kinetic energy ratio. RESULTS: Instantaneous differences in flow and wall shear stress patterns were appreciable, especially for bifurcation aneurysms. Linear regressions revealed strong correlations (R 2 > 0.9) between high-resolution and normal-resolution solutions for all indices except kinetic energy ratio (R2 = 0.25) and oscillatory shear index (R2 = 0.23); however, for most indices, the slopes were significantly <1, reflecting a pronounced underestimation by the normal-resolution simulations. Some high-resolution simulations were highly unstable, with fluctuating wall shear stresses reflected by the poor oscillatory shear index correlation. CONCLUSIONS: Typical computational fluid dynamics solution strategies may ultimately be adequate for augmenting rupture risk assessment on the basis of certain highly reduced indices; however, they cannot be relied on for predicting the magnitude and character of the complex biomechanical stimuli to which the aneurysm wall may be exposed. This impact of the computational fluid dynamics solution strategy is likely greater than that for other modeling assumptions or uncertainties.

Maddison J.R.,University of Edinburgh | Maddison J.R.,University of Oxford | Farrell P.E.,University of Oxford | Farrell P.E.,Center for Biomedical Computing
Computer Methods in Applied Mechanics and Engineering | Year: 2014

Recent advances in high level finite element systems have allowed for the symbolic representation of discretisations and their efficient automated implementation as model source code. This allows for the extremely compact implementation of complex non-linear models in a handful of lines of high level code. In this work we extend the high level finite element FEniCS system to introduce an abstract representation of the temporal discretisation: this enables the similarly rapid development of transient finite element models. Efficiency is achieved via aggressive optimisations that exploit the temporal structure, such as automated pre-assembly and caching of forms, and the robust re-use of matrix factorisations and preconditioner data. The resulting models are as fast or faster than hand-optimised finite element codes. The high level representation of the system remains extremely compact and easily manipulated. This structure is exploited to derive the associated discrete adjoint model automatically, with the adjoint model inheriting the performance advantages of the forward model. Combined, this provides a system for the rapid development of efficient transient models, together with their discrete adjoints. © 2014 Elsevier B.V.

Funke S.W.,Imperial College London | Funke S.W.,Center for Biomedical Computing | Farrell P.E.,University of Oxford | Piggott M.D.,Imperial College London
Renewable Energy | Year: 2014

Oceanic tides have the potential to yield a vast amount of renewable energy. Tidal stream generators are one of the key technologies for extracting and harnessing this potential. In order to extract an economically useful amount of power, hundreds of tidal turbines must typically be deployed in an array. This naturally leads to the question of how these turbines should be configured to extract the maximum possible power: the positioning and the individual tuning of the turbines could significantly influence the extracted power, and hence is of major economic interest. However, manual optimisation is difficult due to legal site constraints, nonlinear interactions of the turbine wakes, and the cubic dependence of the power on the flow speed. The novel contribution of this paper is the formulation of this problem as an optimisation problem constrained by a physical model, which is then solved using an efficient gradient-based optimisation algorithm. In each optimisation iteration, a two-dimensional finite element shallow water model predicts the flow and the performance of the current array configuration. The gradient of the power extracted with respect to the turbine positions and their tuning parameters is then computed in a fraction of the time taken for a flow solution by solving the associated adjoint equations. These equations propagate causality backwards through the computation, from the power extracted back to the turbine positions and the tuning parameters. This yields the gradient at a cost almost independent of the number of turbines, which is crucial for any practical application. The utility of the approach is demonstrated by optimising turbine arrays in four idealised scenarios and a more realistic case with up to 256 turbines in the Inner Sound of the Pentland Firth, Scotland. © 2013 The Authors.

Logg A.,Center for Biomedical Computing | Wells G.N.,University of Cambridge
ACM Transactions on Mathematical Software | Year: 2010

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled, and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This article discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code. © 2010 ACM.

Skallerud B.,Norwegian University of Science and Technology | Prot V.,Center for Biomedical Computing | Nordrum I.S.,Norwegian University of Science and Technology | Nordrum I.S.,St Olavs Hospital
Biomechanics and Modeling in Mechanobiology | Year: 2011

The present study addresses the effect of muscle activation contributions to mitral valve leaflet response during systole. State-of-art passive hyperelastic material modeling is employed in combination with a simple active stress part. Fiber families are assumed in the leaflets: one defined by the collagen and one defined by muscle activation. The active part is either assumed to be orthogonal to the collagen fibers or both orthogonal to and parallel with the collagen fibers (i.e. an orthotropic muscle fiber model). Based on data published in the literature and information herein on morphology, the size of the leaflet parts that contain muscle fibers is estimated. These parts have both active and passive materials, the remaining parts consist of passive material only. Several solid finite element analyses with different maximum activation levels are run. The simulation results are compared to corresponding echocardiography at peak systole for a porcine model. The physiologically correct flat shape of the closed valve is approached as the activation levels increase. The non-physiological bulging of the leaflet into the left atrium when using passive material models is reduced significantly. These results contribute to improved understanding of the physiology of the native mitral valve, and add evidence to the hypothesis that the mitral valve leaflets not are just passive elements moving as a result of hemodynamic pressure gradients in the left part of the heart. © 2010 Springer-Verlag.

Hake J.,Center for Biomedical Computing | Kekenes-Huskey P.M.,Howard Hughes Medical Institute | McCulloch A.D.,University of California at San Diego
Current Opinion in Structural Biology | Year: 2014

Numerous signaling processes in the cell are controlled in microdomains that are defined by cellular structures ranging from nm to μm in size. Recent improvements in microscopy enable the resolution and reconstruction of these micro domains, while new computational methods provide the means to elucidate their functional roles. Collectively these tools allow for a biophysical understanding of the cellular environment and its pathological progression in disease. Here we review recent advancements in microscopy, and subcellular modeling on the basis of reconstructed geometries, with a special focus on signaling microdomains that are important for the excitation contraction coupling in cardiac myocytes. © 2014 Elsevier Ltd.

Evju T.,Center for Biomedical Computing | Valen-Sendstad K.,Center for Biomedical Computing | Valen-Sendstad K.,King's College | Mardal K.-A.,Center for Biomedical Computing
Journal of Biomechanics | Year: 2013

Recent computational fluid dynamics (CFD) studies relate abnormal blood flow to rupture of cerebral aneurysms. However, it is still debated how to model blood flow with sufficient accuracy. Common assumptions made include Newtonian behaviour of blood, traction free outlet boundary conditions and inlet boundary conditions based on available literature. These assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature. However, the consequences of these assumptions have so far been inadequately addressed.This study investigates the effects of 4 different viscosity models, 2 different inflow conditions and 2 different outflow conditions in 12 middle cerebral artery aneurysms. The differences are quantified in terms of 3 different wall shear stress (WSS) metrics, involving maximal WSS, average WSS, and proportion of aneurysm sac area with low WSS. The results were compared with common geometrical metrics such as volume, aspect ratio, size ratio and parent vessel diameter and classifications in terms of sex and aneurysm type.The results demonstrate strong correlations between the different viscosity models and boundary conditions. The correlation between the different WSS metrics range from weak to medium. No strong correlations were found between the different WSS metrics and the geometrical metrics or classifications. © 2013 Elsevier Ltd.

Valen-Sendstad K.,King's College | Valen-Sendstad K.,Center for Biomedical Computing | Mardal K.-A.,Center for Biomedical Computing | Steinman D.A.,King's College
Journal of Biomechanics | Year: 2013

High-frequency flow fluctuations in intracranial aneurysms have previously been reported in vitro and in vivo. On the other hand, the vast majority of image-based computational fluid dynamics (CFD) studies of cerebral aneurysms report periodic, laminar flow. We have previously demonstrated that transitional flow, consistent with in vivo reports, can occur in a middle cerebral artery (MCA) bifurcation aneurysm when ultra-high-resolution direct numerical simulation methods are applied. The object of the present study was to investigate if such high-frequency flow fluctuations might be more widespread in adequately-resolved CFD models. A sample of N=12 anatomically realistic MCA aneurysms (five unruptured, seven ruptured), was digitally segmented from CT angiograms. Four were classified as sidewall aneurysms, the other eight as bifurcation aneurysms. Transient CFD simulations were carried out assuming a steady inflow velocity of 0.5. m/s, corresponding to typical peak systolic conditions at the MCA. To allow for detection of clinically-reported high-frequency flow fluctuations and resulting flow structures, temporal and spatial resolutions of the CFD simulations were in the order of 0.1. ms and 0.1. mm, respectively. A transient flow response to the stationary inflow conditions was found in five of the 12 aneurysms, with energetic fluctuations up to 100. Hz, and in one case up to 900. Hz. Incidentally, all five were ruptured bifurcation aneurysms, whereas all four sidewall aneurysms, including one ruptured case, quickly reached a stable, steady state solution. Energetic, rapid fluctuations may be overlooked in CFD models of bifurcation aneurysms unless adequate temporal and spatial resolutions are used. Such fluctuations may be relevant to the mechanobiology of aneurysm rupture, and to a recently reported dichotomy between predictors of rupture likelihood for bifurcation vs. sidewall aneurysms. © 2012 Elsevier Ltd.

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