Uncertainty quantification in cardiovascular simulation with clinically-informed data uncertainty

Project description

심혈관 시뮬레이션은 최근 심혈관 질병의 진단과 수술 경과의 예측에 점진적으로 적용되고 있습니다. 심혈관 시뮬레이션의 프로세스는 CT/MRI 이미지 데이터로부터 3차원의 심혈관의 해부학적 모델을 구성하고, 이에 인체의 생리학적 조건(Physiologic boundary condition)을 적용한 후 혈류(Blood flow) 및 혈관(Vessel wall)의 생체 역학을 지배하는 편미분방정식들을 수치해석 기법을 통해 푸는 과정으로 진행됩니다. 심혈관 시뮬레이션을 이용하면 혈압(Blood pressure), 혈류량(Flow rate), 혈관이 받는 전단응력(Wall shear stress)값을 비침습적으로(non-invasively) 측정할 수 있습니다. 심장 근육에 피를 공급하는 관상동맥(Coronary artery)에 지방과 콜레스테롤 등이 축적되는 관상동맥경화의 정도를 가늠하여, 심장 질환의 위험도와 수술 여부를 가늠하게 하는 수치인 FFR(Fractional flow reserve)은 인체 내 도관삽입술 (Catetherization)과 조영술(Angiography)을 통해 검사하는 방식으로 측정되어 왔습니다. 최근에 인체에 침투하는 방법을 사용하지 않고도 FFR 수치를 CT/MRI 이미지와 심혈관 시뮬레이션 결과만으로 측정 할수있는 FFR-CT기술이 개발 되었고, 이 기술은 FDA의 승인을 받으며 심혈관질환 수술 계획의 새로운 방법을 제시하고 있습니다. 

심혈관 시뮬레이션을 수행하기 위해서는 수많은 환자 데이터와 생리학적 모델에 공급되는 파라미터들이 필요합니다. 그런데 환자의 데이터는 생리적 반응에 따라 시시각각 바뀌며 데이터 측정 과정에서도 수많은 오류들이 포함되어 있기 때문에, 생명을 다루는 수술에 심혈관 시뮬레이션을 적용할 때 시뮬레이션의 결과값이 얼마만큼의 신뢰도를 가지는지에 대한 평가는 필수적입니다. 그럼에도 불구하고 현재까지 심혈관 시뮬레이션들은 예측값을 신뢰 구간(Confidence interval) 없이 하나의 값으로 제시하는 경우가 많았습니다. 이 연구에서는 불확실성의 정량화법 (Uncertainty quantification)을 심혈관 시뮬레이션에 적용하여, 심혈관 시뮬레이션에 적용되는 입력 데이터의 불확실성과 시뮬레이션의 결과값의 불확실성 사이의 관계를 정량적으로 규명하였습니다. 불확실성의 정량화법은 입력 계수들의 확률 분포에서부터 샘플을 추출하고, 각각의 추출된 샘플들로 부터 심혈관 시뮬레이션을 수행한 후, 시뮬레이션의 결과값들의 확률분포와 기대값, 분산등을 구하는 프로세스로 진행되었습니다. 

Abstract: Cardiovascular simulations offer low risk, non-invasive means to obtain clinically relevant information about the progression of cardiovascular (CV) disease, and to make model-driven decisions regarding treatment options for individual patients. However, a dangerous pitfall of current simulation methods is that they fail to acknowledge or quantify the numerous sources of uncertainty involved in the clinical data assimilation and modeling process. Because of that, current simulations produce deterministic quantities that users are expected to accept as “truth.” This leads to competing claims of accuracy from proponents of different modeling methods, with little means for comparison, and justified skepticism on the part of the medical community. As simulation data are increasingly incorporated into disease research, clinical trials, and the FDA approval process, there is a pressing need to establish strict guidelines for assessing the impact of uncertainty on simulation predictions. The main focus of this work is to apply UQ tools capable of handling clinical data and physiologic uncertainty to cardiovascular simulation.

Publication:
The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls
J. Seo, D. Schiavazzi, A. Kahn, A. Marsden
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, 2020, Vol. 36 (8).

Multi-fidelity uncertainty quantification for coronary artery circulation models

Abstract: 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 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.

Publication:
Multi-fidelity estimators for coronary artery circulation models under clinically-informed data uncertainty
J. Seo, C. Fleeter, A. Kahn, A. Marsden, D. Schiavazzi
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 2020,DOI:10.1615Int.J.UncertaintyQuantification.2020033068

Performance of preconditioned iterative linear solvers for cardiovascular simulations

Abstract: 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 multiscale finite element method. We focus on three approaches: the problem agnostic generalized minimum residual 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, multigrid, 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 preconditioners 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.

Publication:
Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels.
J. Seo, D. Schiavazzi, A. Marsden
COMPUTATIONAL MECHANICS, 2019, Vol. 64, 717-739.

Collaborators: Casey Fleeter (Stanford), Daniele Schiavazzi (Notre Dame), Gianluca Geraci (Sandia National Lab), Andrew Kahn (UCSD), Alison Marsden (Stanford)

Funding Sources: National Institute of Health (NIH), National Science Foundation (NSF).