Uncertainty Quantification for a Blood Pump Device with Generalized Polynomial Chaos Expansion

Nowadays, an increasing number of numerical modeling techniques, notably by means of the finite element method (FEM), are involved in the industrial design process and play a vital role in the area of the biomedical engineering. Particularly, the computational fluid dynamics (CFD) has become a promising tool for investigating the fluid behavior and has also been used to study the cardiovascular hemodynamics to predict the blood flow in the cardiovascular system over the recent decades. However, simulating a fluid in rotational frames is not trivial, as the classical fluid calculation considers that the geometry of the fluid domain does not alter along the time. In the meanwhile, due to the high rotating speed and the complex geometry of the ventricular assist device (VAD), a turbulent flow must be developed inside the pump housing. The Navier-Stokes equations are not applicable in respect of our available computing resource, additional assumptions and approaches are often applied as a means to model the eddy formation and cope with numerical instabilities. For many applications, there is still a big gap between the experimental data and the numerical results. Some of the discrepancies come especially from uncertain data which are used in the physical model, therefore, Uncertainty Quantification (UQ) comes into play. The Galerkin-based polynomial chaos expansion method delivers directly the mean and higher stochastic moments in a closed form. Due to the Galerkin projection’s properties, the spectral convergence is achieved. This thesis is dedicated to developing an efficient model to simulate the blood pump assuming uncertain parametric input sources. In a first step, we develop the shear layer update approach built on the Shear-Slip Mesh Update Method (SSMUM), our proposition facilitates the update procedure in parallel computing by forcing the local vector to retain the same structure. In a second step, we focus on the Variational Multiscale method (VMS) in order to handle the numerical instability and approximate the turbulent behavior in the blood. As a consequence of utilizing the intrusive Polynomial Chaos formulation, a highly coupled system needs to be solved in an efficient manner. Accordingly, we take advantage of the Multilevel preconditioner to precondition our stochastic Galerkin system, in which the Mean-based preconditioner is prescribed to be the smoother. Besides, the mean block is preconditioned with the Schur-Complement method, which leads to an acceleration of the solution process. Hence, by developing and combining the proposed solvers and preconditioners, dealing with a large coupled stochastic fluid problem on a modern computer architecture is then feasible. Furthermore, based on the stochastic solutions obtained from the previous described system, we obtain valuable information about the blood flow accompanied with certain level of confidence, which is beneficial for designing a new blood-handle device or improving the current model

Efficient Uncertainty Quantification in a Multiscale Model of Pulmonary Arterial and Venous Hemodynamics

Computational hemodynamics models are becoming increasingly useful in the management and prognosis of complex, multiscale pathologies, including those attributed to the development of pulmonary vascular disease. However, diseases like pulmonary hypertension are heterogeneous, and affect both the proximal arteries and veins as well as the microcirculation. Simulation tools and the data used for model calibration are also inherently uncertain, requiring a full analysis of the sensitivity and uncertainty attributed to model inputs and outputs. Thus, this study quantifies model sensitivity and output uncertainty in a multiscale, pulse-wave propagation model of pulmonary hemodynamics. Our pulmonary circuit model consists of fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite the sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. Our analyses provide uncertainty in blood pressure, flow, and wave propagation phenomenon, as well as wall shear stress and cyclic stretch, both of which are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal circulation.Comment: 10 Figures, 2 table

Design and execution of a verification, validation, and uncertainty quantification plan for a numerical model of left ventricular flow after LVAD implantation

BACKGROUND: Left ventricular assist devices (LVADs) are implantable pumps that act as a life support therapy for patients with severe heart failure. Despite improving the survival rate, LVAD therapy can carry major complications. Particularly, the flow distortion introduced by the LVAD in the left ventricle (LV) may induce thrombus formation. While previous works have used numerical models to study the impact of multiple variables in the intra-LV stagnation regions, a comprehensive validation analysis has never been executed. The main goal of this work is to present a model of the LV-LVAD system and to design and follow a verification, validation and uncertainty quantification (VVUQ) plan based on the ASME V&V40 and V&V20 standards to ensure credible predictions. METHODS: The experiment used to validate the simulation is the SDSU cardiac simulator, a bench mock-up of the cardiovascular system that allows mimicking multiple operation conditions for the heart-LVAD system. The numerical model is based on Alya, the BSC’s in-house platform for numerical modelling. Alya solves the Navier-Stokes equation with an Arbitrary Lagrangian-Eulerian (ALE) formulation in a deformable ventricle and includes pressure-driven valves, a 0D Windkessel model for the arterial output and a LVAD boundary condition modeled through a dynamic pressure-flow performance curve. The designed VVUQ plan involves: (a) a risk analysis and the associated credibility goals; (b) a verification stage to ensure correctness in the numerical solution procedure; (c) a sensitivity analysis to quantify the impact of the inputs on the four quantities of interest (QoIs) (average aortic root flow , maximum aortic root flow , average LVAD flow , and maximum LVAD flow ); (d) an uncertainty quantification using six validation experiments that include extreme operating conditions. RESULTS: Numerical code verification tests ensured correctness of the solution procedure and numerical calculation verification showed a grid convergence index (GCI)95% <3.3%. The total Sobol indices obtained during the sensitivity analysis demonstrated that the ejection fraction, the heart rate, and the pump performance curve coefficients are the most impactful inputs for the analysed QoIs. The Minkowski norm is used as validation metric for the uncertainty quantification. It shows that the midpoint cases have more accurate results when compared to the extreme cases. The total computational cost of the simulations was above 100 [core-years] executed in around three weeks time span in Marenostrum IV supercomputer. Conclusions This work details a novel numerical model for the LV-LVAD system, that is supported by the design and execution of a VVUQ plan created following recognised international standards. We present a methodology demonstrating that stringent VVUQ according to ASME standards is feasible but computationally expensive.This project was funded in part by the FDA Critical Path Initiative and by an appointment to the Research Participation Program at the Division of Biomedical Physics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, administered by the Oak Ridge Institute for Science, and Education through an interagency agreement between the U.S. Department of Energy and FDA to RAG. MV and AS acknowledge the funding from the project CompBioMed2 (H2020-EU.1.4.1.3. Grant number: 823712), SilicoFCM (H2020-EU.3.1.5. Grant number: 777204), and NEOTEC 2019 - "Generador de Corazones Virtuales" (“Ministerio de Economía y competititvidad”, EXP - 00123159 / SNEO-20191113). AS salary is partially funded by the “Ministerio de Economía y competititvidad” under the Torres Quevedo Program (grant number: PTQ2019-010528). CB salary is partially funded by the Torres Quevedo Program (grant number: PTQ2018-010290). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer ReviewedPostprint (published version

Statistically Sound Verification and Optimization of Black-Box Systems

This thesis discusses two important problems for the design of practical systems under stochastic parameter variations: verification and optimization. Verification is concerned with the safety of a system, i.e., whether a system satisfies its specifications. If not, optimization is applied to tune the design parameters in the system so that the new design is safe. This thesis treats systems as black-boxes, assuming that the systems can be simulated efficiently but without detailed knowledge of the internal workings. It presents a series of simulation-based techniques to solve the problems of design verification and optimization. A notion called statistical soundness is introduced in this thesis, which guarantees that the outcome of the proposed techniques are “statistically certified” in the sense that the probability of drawing a wrong conclusion is bounded. For the problem of verification, this thesis develops a statistically sound model inference (SSMI) approach. SSMI constructs statistically sound models to explain the relationship between the stochastic parameters and the responses of a system. To improve the scalability of SSMI, a sparse approximation algorithm is also introduced. For the problem of optimization, this thesis presents a statistically sound optimization technique, SSMI-opt. SSMI-opt aims to find values of the design parameters for which the system satisfies the specifications. The proposed techniques can be applied to many interesting areas, including analog/mixd-signal circuits, embedded systems, biological systems, and medical devices. This thesis demonstrates the utility of this methodology on several interesting benchmark examples

Uncertainty Quantification for Fluid-Structure Interaction: Application to Aortic Biomechanics

Diseases of the cardiovascular system count to the most common causes of death in the developed countries. There are many open research questions with respect to a better understanding for example of the physiology of the heart and the main arteries or to the determination of the factors for aneurysm or stenosis development of the aorta. Furthermore, on a daily basis, a heart surgeon has to estimate the probability of success for different treatment scenarios as opposed to no intervention. In recent decades, methods of investigation with living probands (in vivo) and artificial experiments (in vitro) have been complemented more and more by computational methods and simulation (in silico). In particular, numerical simulations have the capability to enhance medical imaging modalities with additional information. However, to date, the biomechanical simulation of aortic blood flow given an uncertain data situation represents a major challenge. So far, mostly deterministic models have been used, Yet, measurement data for the configuration of a simulation is subject to measurement inaccuracies. For the choice of model parameters, which are non-measurable in a living body, often imprecise information is available only. In this work, novel development steps for a numerical framework are presented aiming for the simulation and evaluation of aortic biomechanics using methods of Uncertainty Quantification (UQ). The work includes the modelling of the aortic biomechanics as a fluid-structure interaction (FSI) problem with uncertain parameters. By means of a subject-specific workflow, the simulation of different probands, phantoms and, ultimately, patients is enabled. For the solution of the complex partial differential system of equations, they are discretised with the finite element method (FEM) and a novel, parallelly efficient and problem-specific solver is developed. To verify the numerical framework implemented in the course of this work, a novel analytically solvable benchmark for UQ-FSI problems is proposed. Furthermore, the numerical framework is validated by means of a prototypical aortic phantom experiment. Finally, the UQ-FSI simulation enables the evaluation of a stress overload probability. This novel parameter is exemplarily evaluated by means of the simulation of a human aortic bow. Therewith, this work represents a new contribution to aspects of the development of simulation methods for the investigation of aortic biomechanics

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science