Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics

In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure-volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches.

Computational approaches for mechanobiology in cardiovascular development and diseases

The cardiovascular development in vertebrates evolves in response to genetic and mechanical cues. The dynamic interplay among mechanics, cell biology, and anatomy continually shapes the hydraulic networks, characterized by complex, non-linear changes in anatomical structure and blood flow dynamics. To better understand this interplay, a diverse set of molecular and computational tools has been used to comprehensively study cardiovascular mechanobiology. With the continual advancement of computational capacity and numerical techniques, cardiovascular simulation is increasingly vital in both basic science research for understanding developmental mechanisms and disease etiologies, as well as in clinical studies aimed at enhancing treatment outcomes. This review provides an overview of computational cardiovascular modeling. Beginning with the fundamental concepts of computational cardiovascular modeling, it navigates through the applications of computational modeling in investigating mechanobiology during cardiac development. Second, the article illustrates the utility of computational hemodynamic modeling in the context of treatment planning for congenital heart diseases. It then delves into the predictive potential of computational models for elucidating tissue growth and remodeling processes. In closing, we outline prevailing challenges and future prospects, underscoring the transformative impact of computational cardiovascular modeling in reshaping cardiovascular science and clinical practice.

Learning reduced-order models for cardiovascular simulations with graph neural networks

Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience loss in accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 3% for pressure and flow rate, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models while maintaining high efficiency at inference time.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models

PURPOSE

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model.

METHOD

The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation.

RESULTS

The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress.

CONCLUSION

Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

Monitoring variability in parameter estimates for lumped parameter models of the systemic circulation using longitudinal hemodynamic measurements

BACKGROUND

Physics-based cardiovascular models are only recently being considered for disease diagnosis or prognosis in clinical settings. These models depend on parameters representing the physical and physiological properties of the modeled system. Personalizing these parameters may give insight into the specific state of the individual and etiology of disease. We applied a relatively fast model optimization scheme based on common local optimization methods to two model formulations of the left ventricle and systemic circulation. One closed-loop model and one open-loop model were applied. Intermittently collected hemodynamic data from an exercise motivation study were used to personalize these models for data from 25 participants. The hemodynamic data were collected for each participant at the start, middle and end of the trial. We constructed two data sets for the participants, both consisting of systolic and diastolic brachial pressure, stroke volume, and left-ventricular outflow tract velocity traces paired with either the finger arterial pressure waveform or the carotid pressure waveform.

RESULTS

We examined the feasibility of separating parameter estimates for the individual from population estimates by assessing the variability of estimates using the interquartile range. We found that the estimated parameter values were similar for the two model formulations, but that the systemic arterial compliance was significantly different ([Formula: see text]) depending on choice of pressure waveform. The estimates of systemic arterial compliance were on average higher when using the finger artery pressure waveform as compared to the carotid waveform.

CONCLUSIONS

We found that for the majority of participants, the variability of parameter estimates for a given participant on any measurement day was lower than the variability both across all measurement days combined for one participant, and for the population. This indicates that it is possible to identify individuals from the population, and that we can distinguish different measurement days for the individual participant by parameter values using the presented optimization method.

Reallocation of cutaneous and global blood circulation during sauna bathing through a closed-loop model

OBJECTIVE

Sauna bathing (SB) is an important strategy in cardiovascular protection, but there is no mathematical explanation for the reallocation of blood circulation during heat-induced superficial vasodilation. We sought to reveal such reallocation via a simulated hemodynamic model.

METHODS

A closed-loop cardiovascular model with a series of electrical parameters was constructed. The body surface was divided into seven blocks and each block was modeled by a lumped resistance. These resistances were adjusted to increase skin blood flow (SBF), with the aim of reflecting heat-induced vasodilation during SB. Finally, the blood pressure was compared before and after SB, and the blood flow inside the aorta and visceral arteries were also analyzed.

RESULTS

With increasing SBF in this model, the systolic, diastolic, and mean blood pressure in the arterial trunk decreased by 13-29, 18-36, and 19-37 mmHg, respectively. Despite the increase in the peak and mean blood flow in the arterial trunk, the diastolic blood flow reversal in the thoracic and abdominal aortas increased significantly. Nevertheless, the blood supply to the heart, liver, stomach, spleen, kidney, and intestine decreased by at least 25%. Moreover, the pulmonary blood flow increased significantly.

CONCLUSION

Simulated heat-induced cutaneous vasodilation in this model lowers blood pressure, induces visceral ischemia, and promotes pulmonary circulation, suggesting that the present closed-loop model may be able to describe the effect of sauna bathing on blood circulation. However, the increase of retrograde flow in the aortas found in this model deserves further examination.

Neural Network Vessel Lumen Regression for Automated Lumen Cross-Section Segmentation in Cardiovascular Image-Based Modeling

PURPOSE

We accelerate a pathline-based cardiovascular model building method by training machine learning models to directly predict vessel lumen surface points from computed tomography (CT) and magnetic resonance (MR) medical image data.

METHODS

We formulate vessel lumen detection as a regression task using a polar coordiantes representation.

RESULTS

Neural networks trained with our regression formulation allow predictions to be made with significantly higher accuracy than existing methods that identify the vessel lumen through binary pixel classification. The regression formulation enables machine learning models to be trained end-to-end for vessel lumen detection without post-processing steps that reduce accuracy.

CONCLUSION

By employing our models in a pathline-based cardiovascular model building pipeline we substantially reduce the manual segmentation effort required to build accurate cardiovascular models, and reduce the overall time required to perform patient-specific cardiovascular simulations. While our method is applied here for cardiovascular model building it is generally applicable to segmentation of tree-like and tubular structures from image data.

Estimation of left ventricular stroke work based on a large cohort of healthy children

Left ventricular stroke work is an important prognostic marker to analyze cardiac function. Standard values for children are, however, missing. For clinicians, standards can help to improve the treatment decision of heart failures. For engineers, they can help to optimize medical devices. In this study, we estimated the left ventricular stroke work for children based on modeled pressure-volume loops. A lumped parameter model was fitted to clinical data of 340 healthy children. Reference curves for standard values were created over age, weight, and height. Left ventricular volume was measured with 3D echocardiography, while maximal ventricular pressure was approximated with a regression model from the literature. For validation of this method, we used 18 measurements acquired by a conductance catheter in 11 patients. The method demonstrated a low absolute mean difference of 0.033 J (SD: 0.031 J) for stroke work between measurement and estimation, while the percentage error was 21.66 %. According to the resulting reference curves, left ventricular stroke work of newborns has a median of 0.06 J and increases to 1.15 J at the age of 18 years. Stroke work increases over weight and height in a similar trend. The percentile curves depict the distribution. We demonstrate how reference curves can be used for quantification of differences and comparison in patients.

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 (MLMF) 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 (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is 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 single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, 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 such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.

Accelerating cardiovascular model building with convolutional neural networks

The objective of this work is to reduce the user effort required for 2D segmentation when building patient-specific cardiovascular models using the SimVascular cardiovascular modeling software package. The proposed method uses a fully convolutional neural network (FCNN) to generate 2D cardiovascular segmentations. Given vessel pathlines, the neural network generates 2D vessel enhancement images along the pathlines. Thereafter, vessel segmentations are extracted using the marching-squares algorithm, which are then used to construct 3D cardiovascular models. The neural network is trained using a novel loss function, tailored for partially labeled segmentation data. An automated quality control method is also developed, allowing promising segmentations to be selected. Compared with a threshold and level set algorithm, the FCNN method improved 2D segmentation accuracy across several metrics. The proposed quality control approach further improved the average DICE score by 25.8%. In tests with users of SimVascular, when using quality control, users accepted 80% of segmentations produced by the best performing FCNN. The FCNN cardiovascular model building method reduces the amount of manual segmentation effort required for patient-specific model construction, by as much as 73%. This leads to reduced turnaround time for cardiovascular simulations. While the method was used for cardiovascular model building, it is applicable to general tubular structures. Graphical Abstract Proposed FCNN-based cardiovascular model building pipeline. a.) Image data and vessel pathline supplied by the user. b.) Path information is used to extract image pixel intensities in plane perpendicular to the vessel path. c.) 2D images extracted along vessel pathlines are input to the FCNN. d.) FCNN acts on the input images to compute local vessel enhancement images. e.) Vessel enhancement images computed by the FCNN, the pixel values are between 0 and 1 indicating vessel tissue likelihood. f.) The marching-squares algorithm is appliedto each enhanced image to extract the central vessel segmentation. g.) 2D extracted vessel surface points overlayed on original input images. h.) The 2D vessel surface points are transformed back to 3D space. i.) 3D crosssectional vessel surfaces are interpolated along the pathline to form the final vessel model.