Searcharxiv⌕ Search

arXiv subjects

Alison L. Marsden

Publications and source records attributed to Alison L. Marsden.

51 records · Page 3Linked to original sources
arXiv2021

Quantitative Hemodynamics in Aortic Dissection: Comparing in vitro MRI with FSI Simulation in a Compliant Model

The analysis of quantitative hemodynamics and luminal pressure may add valuable information to aid treatment strategies and prognosis for aortic dissections. This work directly compared in vitro 4D-flow magnetic resonance imaging (MRI), catheter-based pressure measurements, and computational fluid dynamics that integrated fluid-structure interaction (CFD FSI). Experimental data was acquired with a compliant 3D-printed model of a type-B aortic dissection (TBAD) that was embedded into a physiologically tuned flow circuit. In vitro flow and pressure information were used to tune the CFD FSI Windkessel boundary conditions. Results showed very good overall agreement of complex flow patterns, true to false lumen flow splits, and pressure distribution. This work demonstrates feasibility of a tunable experimental setup that integrates a patient-specific compliant model and provides a test bed for exploring critical imaging and modeling parameters that ultimately may improve the prognosis for patients with aortic dissections.

physics.flu-dyn↗
arXiv2021

A continuum and computational framework for viscoelastodynamics: finite deformation linear models

This work concerns the continuum basis and numerical formulation for deformable materials with viscous dissipative mechanisms. We derive a viscohyperelastic modeling framework based on fundamental thermomechanical principles. Since most large deformation problems exhibit the isochoric property, our modeling work is constructed based on the Gibbs free energy in order to develop a continuum theory using the pressure-primitive variables, which is known to be well-behaved in the incompressible limit. With a general theory presented, we focus on a family of free energies that leads to the so-called finite deformation linear model. Our derivation elucidates the origin of the evolution equations of that model, which was originally proposed heuristically. In our derivation, the thermodynamic inconsistency is clarified and rectified. We then discuss the relaxation property of the non-equilibrium stress in the thermodynamic equilibrium limit and its implication on the form of free energy. A modified version of the identical polymer chain model is then proposed, with a special case being the model proposed by G. Holzapfel and J. Simo. Based on the consistent modeling framework, a provably energy stable numerical scheme is constructed for incompressible viscohyperelasticity using inf-sup stable elements. In particular, we adopt a suite of smooth generalization of the Taylor-Hood element based on Non-Uniform Rational B-Splines (NURBS) for spatial discretization. The temporal discretization is performed via the generalized-alpha scheme. We present a suite of numerical results to corroborate the proposed numerical properties, including the nonlinear stability, robustness under large deformation, and the stress accuracy resolved by the higher-order elements.

math.NA↗
arXiv2021

On the periodicity of cardiovascular fluid dynamics simulations

Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no standardized method to determine whether a simulation has yet reached that periodic state. In this work, we propose use of the asymptotic error measure to quantify the difference between simulation results and their ideal periodic state using lumped-parameter modeling. We further show that initial conditions are crucial in reducing computational time and develop an automated framework to generate appropriate initial conditions from a one-dimensional model of blood flow. We demonstrate the performance of our initialization method using six patient-specific models from the Vascular Model Repository. In our examples, our initialization protocol achieves periodic convergence within one or two cardiac cycles, leading to a significant reduction in computational cost compared to standard methods. All computational tools used in this work are implemented in the open-source software platform SimVascular. Automatically generated initial conditions have the potential to significantly reduce computation time in cardiovascular fluid dynamics simulations.

cs.CE↗
arXiv2020

Multi-fidelity estimators for coronary circulation models under clinically-informed data uncertainty

Numerical models are increasingly used for non-invasive diagnosis and treatment planning in coronary artery disease, where service-based technologies have proven successful in identifying hemodynamically significant and hence potentially dangerous vascular anomalies. Despite recent progress towards clinical adoption, many results in the field are still based on a deterministic characterization of blood flow, with no quantitative assessment of the variability of simulation outputs due to uncertainty from multiple sources. In this study, we focus on parameters that are essential to construct accurate patient-specific representations of the coronary circulation, such as aortic pressure waveform, intramyocardial pressure and quantify how their uncertainty affects clinically relevant model outputs. We construct a deformable model of the left coronary artery subject to a prescribed inlet pressure and with open-loop outlet boundary conditions, treating fluid-structure interaction through an Arbitrary-Lagrangian-Eulerian frame of reference. Random input uncertainty is estimated directly from repeated clinical measurements from intra-coronary catheterization and complemented by literature data. We also achieve significant computational cost reductions in uncertainty propagation thanks to multifidelity Monte Carlo estimators of the outputs of interest, leveraging the ability to generate, at practically no cost, one- and zero-dimensional low-fidelity representations of left coronary artery flow, with appropriate boundary conditions. The results demonstrate how the use of multi-fidelity control variate estimators leads to significant reductions in variance and accuracy improvements with respect to traditional Monte-Carlo.

physics.med-ph↗
arXiv2020

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these low-fidelity and high-fidelity models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. We seek to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to Monte Carlo and multilevel Monte Carlo estimators based only on three-dimensional simulations. We demonstrate significant reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities and healthy models show larger reductions than local quantities and diseased model, as the latter rely more heavily on the highest fidelity model evaluations. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.

q-bio.QM↗
arXiv2020

A note on the accuracy of the generalized-$α$ scheme for the incompressible Navier-Stokes equations

We investigate the temporal accuracy of two generalized-$α$ schemes for the incompressible Navier-Stokes equations. The conventional approach treats the pressure with the backward Euler method while discretizing the remainder of the Navier-Stokes equations with the generalized-$α$ method. We developed a suite of numerical codes using inf-sup stable higher-order non-uniform rational B-spline (NURBS) elements for spatial discretization. In doing so, we are able to achieve very high spatial accuracy and, furthermore, to perform temporal refinement without consideration of the stabilization terms, which can degenerate for small time steps. Numerical experiments suggest that only first-order accuracy is achieved, at least for the pressure, in this aforesaid approach. Evaluating the pressure at the intermediate time step recovers second-order accuracy, and the numerical implementation, in fact, becomes simpler. Therefore, although the pressure can be viewed as a Lagrange multiplier enforcing the incompressibility constraint, its temporal discretization is not independent and should be subject to the generalized-$α$ method in order to maintain second-order accuracy of the overall algorithm.

math.NA↗
arXiv2020

A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction

We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear continuum mechanics. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization. We first consider the continuum body instantiated as a hyperelastic material and develop a variational multiscale formulation for the hyper-elastodynamic problem. The generalized-alpha method is applied for temporal discretization. A segregated algorithm for the nonlinear solver is designed and carefully analyzed. Second, we apply the new formulation to construct a novel unified formulation for fluid-solid coupled problems. The variational multiscale formulation is utilized for spatial discretization in both fluid and solid subdomains. The generalized-alpha method is applied for the whole continuum body, and optimal high-frequency dissipation is achieved in both fluid and solid subproblems. A new predictor multi-corrector algorithm is developed based on the segregated algorithm to attain a good balance between robustness and efficiency. The efficacy of the new formulations is examined in several benchmark problems. The results indicate that the proposed modeling and numerical methodologies constitute a promising technology for biomedical and engineering applications, particularly those necessitating incompressible models.

physics.comp-ph↗
arXiv2020

The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls

Cardiovascular simulations are increasingly used for non-invasive diagnosis of cardiovascular disease, to guide treatment decisions, and in the design of medical devices. Quantitative assessment of the variability of simulation outputs due to input uncertainty is a key step toward further integration of cardiovascular simulations in the clinical workflow. In this study, we present uncertainty quantification in computational models of the coronary circulation to investigate the effect of uncertain parameters, including coronary pressure waveform, intramyocardial pressure, morphometry exponent, and the vascular wall Young's modulus. We employ a left coronary artery model with deformable vessel walls, simulated via an ALE framework for FSI, with a prescribed inlet pressure and open-loop lumped parameter network outlet boundary conditions. Stochastic modeling of the uncertain inputs is determined from intra-coronary catheterization data or gathered from the literature. Uncertainty propagation is performed using several approaches including Monte Carlo, Quasi MC, stochastic collocation, and multiwavelet stochastic expansion. Variabilities in QoI, including branch pressure, flow, wall shear stress, and wall deformation are assessed. We find that uncertainty in inlet pressures and intramyocardial pressures significantly affect all resulting QoIs, while uncertainty in elastic modulus only affects the mechanical response of the vascular wall. Variability in the morphometry exponent has little effect on coronary hemodynamics or wall mechanics. Finally, we compare convergence behaviors of statistics of QoIs using several uncertainty propagation methods. From the simulation results, we conclude that the multi-wavelet stochastic expansion shows superior accuracy and performance against Quasi Monte Carlo and stochastic collocation methods.

physics.med-ph↗
arXiv2020

Fluid-structure interaction modeling of blood flow in the pulmonary arteries using the unified continuum and variational multiscale formulation

In this work, we present a computational fluid-structure interaction (FSI) study for a healthy patient-specific pulmonary arterial tree using the unified continuum and variational multiscale (VMS) formulation we previously developed. The unified framework is particularly well-suited for FSI, as the fluid and solid sub-problems are addressed in essentially the same manner and can thus be uniformly integrated in time with the generalized-$α$ method. In addition, the VMS formulation provides a mechanism for large-eddy simulation in the fluid sub-problem and pressure stabilization in the solid sub-problem. The FSI problem is solved in a quasi-direct approach, in which the pressure and velocity in the unified continuum body are first solved, and the solid displacement is then obtained via a segregated algorithm and prescribed as a boundary condition for the mesh motion. Results of the pulmonary arterial FSI simulation are presented and compared against those of a rigid wall simulation.

physics.comp-ph↗
arXiv2019

The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations

We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the generalized-$α$ scheme. The spatiotemporal discretization leads to a block structure of the resulting consistent tangent matrix in the Newton-Raphson procedure. As a generalization of the conventional block preconditioners, a three-level nested block preconditioner is introduced to attain a better representation of the Schur complement, which plays a key role in the overall algorithm robustness and efficiency. This approach provides a flexible, algorithmic way to handle the Schur complement for problems involving multiscale and multiphysics coupling. The solution method is implemented and benchmarked against experimental data from the nozzle challenge problem issued by the US Food and Drug Administration. The robustness, efficiency, and parallel scalability of the proposed technique are then examined in several settings, including moderately high Reynolds number flows and physiological flows with strong resistance effect due to coupled downstream vasculature models. Two patient-specific hemodynamic simulations, covering systemic and pulmonary flows, are performed to further corroborate the efficacy of the proposed methodology.

math.NA↗
arXiv2019

Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels

Computing the solution of linear systems of equations is invariably the most time consuming task in the numerical solutions of PDEs in many fields of computational science. In this study, we focus on the numerical simulation of cardiovascular hemodynamics with rigid and deformable walls, discretized in space and time through the variational multi-scale finite element method. We focus on three approaches: the problem agnostic generalized minimum residual (GMRES) and stabilized bi-conjugate gradient (BICGS) methods, and a recently proposed, problem specific, bi-partitioned (BIPN) method. We also perform a comparative analysis of several preconditioners, including diagonal, block-diagonal, incomplete factorization, multi-grid, and resistance based methods. Solver performance and matrix characteristics (diagonal dominance, symmetry, sparsity, bandwidth and spectral properties) are first examined for an idealized cylindrical geometry with physiologic boundary conditions and then successively tested on several patient-specific anatomies representative of realistic cardiovascular simulation problems. Incomplete factorization pre-conditioners provide the best performance and results in terms of both strong and weak scalability. The BIPN method was found to outperform other methods in patient-specific models with rigid walls. In models with deformable walls, BIPN was outperformed by BICG with diagonal and Incomplete LU preconditioners.

physics.comp-ph↗
arXiv2018

An energy-stable mixed formulation for isogeometric analysis of incompressible hyper-elastodynamics

We develop a mixed formulation for incompressible hyper-elastodynamics based on a continuum modeling framework recently developed and smooth generalizations of the Taylor-Hood element based on non-uniform rational B-splines (NURBS). This continuum formulation draws a link between computational fluid dynamics and computational solid dynamics. This link inspires an energy stability estimate for the spatial discretization, which favorably distinguishes the formulation from the conventional mixed formulations for finite elasticity. The inf-sup condition is utilized to provide a bound for the pressure field. The generalized-$α$ method is applied for temporal discretization, and a nested block preconditioner is invoked for the solution procedure. The inf-sup stability for different pairs of NURBS elements is elucidated through numerical assessment. The convergence rate of the proposed formulation with various combinations of mixed elements is examined by the manufactured solution method. The numerical scheme is also examined under compressive and tensile loads for isotropic and anisotropic hyperelastic materials. Finally, a suite of dynamic problems is numerically studied to corroborate the stability and conservation properties.

math.NA↗
arXiv2018

A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning

We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the generalized-$α$ method. Within the nonlinear solution procedure, a block factorization is performed for the consistent tangent matrix to decouple the kinematics from the balance laws. Within the linear solution procedure, another block factorization is performed to decouple the mass balance equation from the linear momentum balance equations. A nested block preconditioning technique is proposed to combine the Schur complement reduction approach with the fully coupled approach. This preconditioning technique, together with the Krylov subspace method, constitutes a novel iterative method for solving hyper-elastodynamics. We demonstrate the efficacy of the proposed preconditioning technique by comparing with the SIMPLE preconditioner and the one-level domain decomposition preconditioner. Two representative examples are studied: the compression of an isotropic hyperelastic cube and the tensile test of a fully-incompressible anisotropic hyperelastic arterial wall model. The robustness with respect to material properties and the parallel performance of the preconditioner are examined.

math.NA↗
arXiv2010

A Primer on Computational Simulation in Congenital Heart Disease for the Clinician

Interest in the application of engineering methods to problems in congenital heart disease has gained increased popularity over the past decade. The use of computational simulation to examine common clinical problems including single ventricle physiology and the associated surgical approaches, the effects of pacemaker implantation on vascular occlusion, or delineation of the biomechanical effects of implanted medical devices is now routinely appearing in clinical journals within all pediatric cardiovascular subspecialties. In practice, such collaboration can only work if both communities understand each other's methods and their limitations. This paper is intended to facilitate this communication by presenting in the context of congenital heart disease (CHD) the main steps involved in performing computational simulation-from the selection of an appropriate clinical question/problem to understanding the computational results, and all of the "black boxes" in between. We examine the current state of the art and areas in need of continued development. For example, medical image-based model-building software has been developed based on numerous different methods. However, none of them can be used to construct a model with a simple "click of a button". The creation of a faithful, representative anatomic model, especially in pediatric subjects, often requires skilled manual intervention. In addition, information from a second imaging modality is often required to facilitate this process. We describe the technical aspects of model building, provide a definition of some of the most commonly used terms and techniques (e.g. meshes, mesh convergence, Navier-Stokes equations, and boundary conditions), and the assumptions used in running the simulations. Particular attention is paid to the assignment of boundary conditions as this point is of critical importance in the current areas of research within the realm of congenital heart disease. Finally, examples are provided demonstrating how computer simulations can provide an opportunity to "acquire" data currently unobtainable by other modalities, with essentially no risk to patients. To illustrate these points, novel simulation examples of virtual Fontan conversion (from preoperative data to predicted postoperative state) and outcomes of different surgical designs are presented. The need for validation of the currently employed techniques and predicted results are required and the methods remain in their infancy. While the daily application of these technologies to patient-specific clinical scenarios likely remains years away, the ever increasing interest in this area among both clinicians and engineers makes its eventual use far more likely than ever before and, some could argue, only a matter of [computing] time.

physics.med-ph↗