Cardiovascular disease is the leading cause of death worldwide, and heart disease alone is responsible for one in four deaths in the U.S. Congenital heart disease in children is the primary reason for infant mortality and affects roughly one percent of U.S. births, with more than half of patients requiring at least one invasive surgery during their lifetime. The complex interplay of mechanical stimuli (blood flow, mechanical forces) acting on tissues, and the subsequent biological responses, influence cardiovascular disease. Altered pressure and flow lead to extensive remodeling of vascular and cardiac morphology and wall properties. These interactions are crucial to progression of coronary artery disease, bypass graft failure, cardiomyopathy, pulmonary hypertension, cardiac development, and congenital heart disease. Computational modeling can noninvasively quantify blood flow and pressure in image-based models for individual patients, and is increasingly able to capture biological responses to changing mechanical forces. One can use these models to determine the impact of mechanical forces on disease progression and in virtual treatment planning for personalized medicine.
Partnerships between engineers and clinicians have yielded numerous advances in the treatment of adult and pediatric cardiovascular disease. One prominent example is the development of the first battery-operated wearable pacemaker, pioneered by surgeon Clarence Walton Lillehei and electrical engineer/TV repairman Earl E. Bakken. Engineering-clinical collaborations have also resulted in other high-impact technologies, such as cardiopulmonary bypass, coronary stents and balloon angioplasty, advanced medical imaging techniques, and transcatheter devices to treat structural diseases. Over the past decade, cardiovascular blood flow simulation has emerged as one of the most dynamic examples of this critical partnership, and is now poised to significantly impact cardiovascular patient care.
Computational models of blood flow were first developed for pediatric cardiology in the late 1980s, and initially combined idealized anatomic models with computational fluid dynamics (CFD) simulations. CFD quickly influenced surgical practice for those born with a severe form of single-ventricle congenital heart disease, in which patients are missing half of their heart at birth . The introduction of patient-specific modeling—where anatomic models are reconstructed from medical image data—subsequently allowed blood flow simulations in customized anatomic models for individual patients . High-performance computing and numerical analysis tools developed in the fluid dynamics and aerospace communities enabled fast parallel solution of the Navier-Stokes equations — the partial differential equations (PDEs) governing blood flow. Recent clinical trials demonstrate that CFD simulations of coronary flow—coupled with physiologic models—can noninvasively predict fractional flow reserve, a measure of the severity of coronary blockages caused by atherosclerotic plaques .
Cardiovascular simulations fill several crucial gaps in current clinical capabilities. First, while predictive simulations are now used routinely in aerospace and other engineering industries, the medical field still relies primarily on statistical outcomes and trial-and-error approaches to advance surgical methods. Simulations now offer a powerful way to predict surgical outcomes, systematically test and optimize new surgical approaches and devices, perform risk stratification, and personalize treatments for individual patients. Second, one can use simulations to characterize the in vivo mechanical environment, providing crucial hemodynamics and mechanical stimuli data that is not readily attainable from medical imaging. This data is a key component of the mechanobiological puzzle relating the mechanical environment to subsequent disease progression.
One can model blood flow in the cardiovascular system with varying levels of fidelity, typically trading computational cost for spatial and temporal resolution (see Figure 1). The simplest of these are zero-dimensional lumped parameter circuit models, which are governed by ordinary differential equations. They are surprisingly effective at capturing vital features of cardiovascular physiology and heart function, producing realistic pressure-volume loops and flow and pressure waveforms. But they lack spatial information. One can include limited spatial information in intermediate-complexity one-dimensional models, which integrate the full PDEs over the blood vessel cross-section and produce a reduced one-dimensional system with unknowns of flow rate and cross-sectional area, together with constitutive material models. The resulting system captures vessel wall deformation and wave propagation with more realistic geometry and one spatial dimension, and is usable in extensive “full-body” models of the cardiovascular system. Finally, one can solve the full three-dimensional equations by discretizing the Navier-Stokes equations with finite-element or finite-volume methods and fully resolving pressure and velocity at every spatial point in a three-dimensional, patient-specific anatomic model. These models produce high-fidelity spatial and temporal data, but typically require large computations and are thus limited to local anatomical regions.
Figure 1. Multi-fidelity models of the cardiovascular system include zero-dimensional ordinary differential equation models using lumped parameter circuit elements, one-dimensional partial differential equation (PDE) models that capture wall deformation and wave propagation at reduced computational cost, and full three-dimensional PDE models that provide high-fidelity resolved simulations of velocity and pressure in anatomic models. Figure courtesy of the Cardiovascular Biomechanics Computation Lab at Stanford University.
Despite the aforementioned advances, there is an increasing need to incorporate multiphysics models and biological responses into computational predictions of cardiovascular disease. The field is thus undergoing a paradigm shift to move beyond “pure” CFD towards validated models that integrate mechanobiological mechanisms and whole-heart physiology. This capability will be key to understanding, predicting, and altering cardiovascular disease progression. Researchers have recently paid much attention to the advancement of fluid structure interaction methods to capture large deformations in the heart and valves, and more realistic material models for biological tissues with good computational efficiency. One can expand these efforts to whole-heart modeling, including heart contraction and electrophysiology.
Compared to traditional CFD models, these methods pose additional challenges of multiple time and spatial scales, multiple parameters, and the need for fast cardiac image segmentation. Further efforts have attempted to couple CFD with vascular growth and remodeling to capture the interplay of mechanical forces, such as wall shear stress and pressure with the vessel wall’s mechanobiologic response. These forces lead to changes in vessel morphology and composition. Disparate time scales; complex geometries; and inhomogenous, viscoelastic, incompressible biological tissues give rise to further computational and methodological challenges. Finally, scientists are developing thrombosis models to measure the complex series of chemical reactions that comprise the blood coagulation cascade.
The use of uncertainty quantification as a systematic framework for handling uncertain clinical data in model inputs has also garnered recent attention. Researchers accomplish this via parameter estimation to determine model parameter distribution from clinical data, and uncertainty propagation to produce output statistics on quantities of interest. Model parameters are tuned to match the clinical data for individual patients, enabling the computation of personalized output statistics. Additionally, multi-fidelity models—leveraging the aforementioned zero-dimensional and one-dimensional models—have shown recent promise in the convergence acceleration of output statistics and computational cost reduction .
Figure 2. Pre- and post-operative models and simulated velocity demonstrating virtual surgical planning in the pulmonary arteries of pediatric patients with pulmonary stenosis caused by Alagille syndrome. Image courtesy of .
The above directions can potentially enable application of predictive simulations to increasingly complex and high-impact clinical problems. Using patient-specific simulations and vascular growth and remodeling, our group has recently hypothesized new mechanisms for the prevention of vein graft failure after coronary artery bypass graft surgery [4, 5]. Recent work has also yielded predictive growth and remodeling models for tissue-engineered bypass grafts, which surgeons are currently implanting in pediatric patients with single-ventricle physiology . Practitioners have used simple models of right ventricular stroke work to risk-stratify pediatric patients with pulmonary hypertension and predict their need for heart transplants. Virtual surgery has likewise been effective in predicting the need to relieve pulmonary stenosis in pediatric patients with Alagille syndrome (see Figure 2) . Future clinical applications that will leverage the aforesaid efforts in integrative modeling will include hypertrophic cardiomyopathy, surgical planning in pulmonary reconstructive surgery for congenital heart patients, thrombotic risk in devices and grafts, and aortic dissection. It is crucial that such applications continue to drive the development of new computational technologies, including multiscale modeling, fast image segmentation, linear solver technology, and uncertainty quantification.
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