Uncertainty quantification implementations in human hemodynamic flows

Observer- and sequence variability in personalized 4D flow MRI-based cardiovascular models

Subject-specific parameters in lumped hemodynamic models of the cardiovascular system can be estimated using data from experimental measurements, but the parameter estimation may be hampered by the variability in the input data. In this study, we investigate the influence of inter-sequence, intra-observer, and inter-observer variability in input parameters on estimation of subject-specific model parameters using a previously developed approach for model-based analysis of data from 4D Flow MRI acquisitions and cuff pressure measurements. The investigated parameters describe left ventricular time-varying elastance and aortic compliance. Parameter reproducibility with respect to variability in the MRI input measurements was assessed in a group of ten healthy subjects. The subject-specific parameters had coefficient of variations between 2.6 and 35% in the intra- and inter-observer analysis. In comparing parameters estimated using data from the two MRI sequences, the coefficients of variation ranged between 3.3 and 41%. The diastolic time constant of the left ventricle and the compliance of the ascending aorta were the parameters with the lowest and the highest variability, respectively. In conclusion, the modeling approach allows for estimating left ventricular elastance parameters and aortic compliance from non-invasive measurements with good to moderate reproducibility concerning intra-user, inter-user, and inter-sequence variability in healthy subjects.

Computational framework for the generation of one-dimensional vascular models accounting for uncertainty in networks extracted from medical images

One-dimensional (1D) cardiovascular models offer a non-invasive method to answer medical questions, including predictions of wave-reflection, shear stress, functional flow reserve, vascular resistance and compliance. This model type can predict patient-specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty in in vivo imaging introduces variability in network size and vessel dimensions, affecting haemodynamic predictions. Understanding the influence of variation in image-derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three-dimensional surfaces and construct vessel centrelines. Still, there is no exact way to generate vascular trees from the centrelines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labelled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D haemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore haemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analysing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high-fidelity patient-specific haemodynamics models. KEY POINTS: This study introduces novel algorithms for generating labelled directed trees from medical images, focusing on accurate junction node placement and radius extraction using change points to provide haemodynamic predictions with uncertainty within expected measurement error. Geometric features, such as vessel dimension (length and radius) and network size, significantly impact pressure and flow predictions in both pulmonary and aortic arterial networks. Standardizing networks to a consistent number of vessels is crucial for meaningful comparisons and decreases haemodynamic uncertainty. Change points are valuable to understanding structural transitions in vascular data, providing an automated and efficient way to detect shifts in vessel characteristics and ensure reliable extraction of representative vessel radii.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

The ocular mathematical virtual simulator: A validated multiscale model for hemodynamics and biomechanics in the human eye

We present our continuous efforts from a modeling and numerical viewpoint to develop a powerful and flexible mathematical and computational framework called Ocular Mathematical Virtual Simulator (OMVS). The OMVS aims to solve problems arising in biomechanics and hemodynamics within the human eye. We discuss our contribution towards improving the reliability and reproducibility of computational studies by performing a thorough validation of the numerical predictions against experimental data. The OMVS proved capable of simulating complex multiphysics and multiscale scenarios motivated by the study of glaucoma. Furthermore, its modular design allows the continuous integration of new models and methods as the research moves forward, and supports the utilization of the OMVS as a promising non-invasive clinical investigation tool for personalized research in ophthalmology.

A Low-Cost Algorithm for Uncertainty Quantification Simulations of Steady-State Flows: Application to Ocular Hemodynamics

An algorithm for the calculation of steady-state flowing under uncertain conditions is introduced in this work in order to obtain a probabilistic distribution of uncertain problem parameters. This is particularly important for problems with increased uncertainty, as typical deterministic methods are not able to fully describe all possible flow states of the problem. Standard methods, such as polynomial expansions and Monte Carlo simulations, are used for the formation of the generalized problem described by the incompressible Navier-Stokes equations. Since every realization of the uncertainty parameter space is coupled with non-linear terms, an incremental iterative procedure was adopted for the calculation. This algorithm adopts a Jacobi-like iteration methodology to decouple the equations and solve them one by one until there is overall convergence. The algorithm was tested in a typical artery geometry, including a bifurcation with an aneurysm, which consists of a well-documented biological flow test case. Additionally, its dependence on the uncertainty parameter space, i.e., the inlet velocity distribution, the Reynolds number variation, and parameters of the procedure, i.e., the number of polynomial expansions, was studied. Symmetry exists in probabilistic theories, similar to the one adopted by the present work. The results of the simulations conducted with the present algorithm are compared against the same but unsteady flow with a time-dependent inlet velocity profile, which represents a typical cardiac cycle. It was found that the present algorithm is able to correctly describe the flow field, as well as capture the upper and lower limits of the velocity field, which was made periodic. The comparison between the present algorithm and the typical unsteady one presented a maximum error of ≈2% in the common carotid area, while the error increased significantly inside the bifurcation area. Moreover, “sensitive” areas of the geometry with increased parameter uncertainty were identified, a result that is not possible to be obtained while using deterministic algorithms. Finally, the ability of the algorithm to tune the parameter limits was successfully tested.

Modelling coronary flows: impact of differently measured inflow boundary conditions on vessel-specific computational hemodynamic profiles

BACKGROUND AND OBJECTIVES

The translation of hemodynamic quantities based on wall shear stress (WSS) or intravascular helical flow into clinical biomarkers of coronary atherosclerotic disease is still hampered by the assumptions/idealizations required by the computational fluid dynamics (CFD) simulations of the coronary hemodynamics. In the resulting budget of uncertainty, inflow boundary conditions (BCs) play a primary role. Accordingly, in this study we investigated the impact of the approach adopted for in vivo coronary artery blood flow rate assessment on personalized CFD simulations where blood flow rate is used as inflow BC.

METHODS

CFD simulations were carried out on coronary angiograms by applying personalized inflow BCs derived from four different techniques assessing in vivo surrogates of flow rate: continuous thermodilution, intravascular Doppler, frame count-based 3D contrast velocity, and diameter-based scaling law. The impact of inflow BCs on coronary hemodynamics was evaluated in terms of WSS- and helicity-based quantities.

RESULTS

As main findings, we report that: (i) coronary flow rate values may differ based on the applied flow derivation technique, as continuous thermodilution provided higher flow rate values than intravascular Doppler and diameter-based scaling law (p = 0.0014 and p = 0.0023, respectively); (ii) such intrasubject differences in flow rate values lead to different surface-averaged values of WSS magnitude and helical blood flow intensity (p<0.0020); (iii) luminal surface areas exposed to low WSS and helical flow topological features showed robustness to the flow rate values.

CONCLUSIONS

Although the absence of a clinically applicable gold standard approach prevents a general recommendation for one coronary blood flow rate derivation technique, our findings indicate that the inflow BC may impact computational hemodynamic results, suggesting that a standardization would be desirable to provide comparable results among personalized CFD simulations of the coronary hemodynamics.

A fast tool for the parametric analysis of human body exposed to LF electromagnetic fields in biomedical applications

A numerical procedure for analyzing electromagnetic (EM) fields interactions with biological tissues is presented. The proposed approach aims at drastically reducing the computational burden required by the repeated solution of large scale problems involving the interaction of the human body with EM fields, such as in the study of the time evolution of EM fields, uncertainty quantification, and inverse problems. The proposed volume integral equation (VIE), focused on low frequency applications, is a system of integral equations in terms of current density and scalar potential in the biological tissues excited by EM fields and/or electrodes connected to the human body. The proposed formulation requires the voxelization of the human body and takes advantage of the regularity of such discretization by speeding-up the computational procedure. Moreover, it exploits recent advancements in the solution of VIE by means of iterative preconditioned solvers and ad hoc parametric Model Order Reduction techniques. The efficiency of the proposed tool is demonstrated by applying it to a couple of realistic model problems: the assessment of the peripheral nerve stimulation, performed in terms of evaluation of the induced electric field, due to the gradient coils of a magnetic resonance imaging scanner during a clinical examination and the assessment of the exposure to environmental fields at 50 Hz of live-line workers with uncertain properties of the biological tissues. Thanks to the proposed method, uncertainty quantification analyses and time domain simulations are possible even for large scale problems and they can be performed on standard computers and reasonable computation time. Sample implementation of the method is made publicly available at https://github.com/UniPD-DII-ETCOMP/BioMOR.

Building robust pathology image analyses with uncertainty quantification

BACKGROUND AND OBJECTIVE

Computerized pathology image analysis is an important tool in research and clinical settings, which enables quantitative tissue characterization and can assist a pathologist's evaluation. The aim of our study is to systematically quantify and minimize uncertainty in output of computer based pathology image analysis.

METHODS

Uncertainty quantification (UQ) and sensitivity analysis (SA) methods, such as Variance-Based Decomposition (VBD) and Morris One-At-a-Time (MOAT), are employed to track and quantify uncertainty in a real-world application with large Whole Slide Imaging datasets - 943 Breast Invasive Carcinoma (BRCA) and 381 Lung Squamous Cell Carcinoma (LUSC) patients. Because these studies are compute intensive, high-performance computing systems and efficient UQ/SA methods were combined to provide efficient execution. UQ/SA has been able to highlight parameters of the application that impact the results, as well as nuclear features that carry most of the uncertainty. Using this information, we built a method for selecting stable features that minimize application output uncertainty.

RESULTS

The results show that input parameter variations significantly impact all stages (segmentation, feature computation, and survival analysis) of the use case application. We then identified and classified features according to their robustness to parameter variation, and using the proposed features selection strategy, for instance, patient grouping stability in survival analysis has been improved from in 17% and 34% for BRCA and LUSC, respectively.

CONCLUSIONS

This strategy created more robust analyses, demonstrating that SA and UQ are important methods that may increase confidence digital pathology.

Comparison of stenosis models for usage in the estimation of pressure gradient across aortic coarctation

Non-invasive estimation of the pressure gradient in cardiovascular stenosis has much clinical importance in assisting the diagnosis and treatment of stenotic diseases. In this research, a systematic comparison is conducted to investigate the accuracy of a group of stenosis models against the MRI- and catheter-measured patient data under the aortic coarctation condition. Eight analytical stenosis models, including six from the literature and two proposed in this study, are investigated to examine their prediction accuracy against the clinical data. The two improved models proposed in this study consider comprehensively the Poiseuille loss, the Bernoulli loss in its exact form, and the entrance effect, of the blood flow. Comparison of the results shows that one of the proposed models demonstrates a cycle-averaged mean prediction error of -0.15 ± 3.03 mmHg, a peak-to-peak prediction error of -1.8 ± 6.89 mmHg, which is the best among the models studied.