Computational fluid dynamics models and congenital heart diseases

Greater than the sum of its parts: multimodality imaging in adults with congenital heart disease

As the population of adults with congenital heart disease (ACHD) grows, there also grows an expanded need for non-invasive surveillance methods to guide management and intervention. A multimodal imaging approach layers complementary insights from echocardiography, computed tomography (CT), magnetic resonance imaging (MRI), and other modalities into a clinician's view of patient physiology. Merely applying strategies from acquired adult cardiac disease would be inadequate and potentially misleading. As data amasses in this small but growing population, investigators in the field of ACHD have discovered population-specific imaging biomarkers that identify deterioration and pivotal time points where intervention may reduce morbidity and mortality. Moreover, due to the variety of physiologies and the modest number of ACHD patients relative to that of adults with acquired heart disease, multicenter registries will be key in advancing research. The integration of well-defined imaging variables into these databases can help identify important biomarkers. Emerging technologies like computational fluid dynamics (CFD) and artificial intelligence (AI) are also primed to enhance imaging capabilities and clinical workflows, though require careful adaption as ACHD patients are not meaningfully represented in the training data for these technologies. Ultimately, a multimodal imaging approach is essential for optimizing care for ACHD patients, enabling personalized medicine where interventions can be performed before clinical deterioration occurs.

Hemodynamics in a three-dimensional printed aortic model: a comparison of four-dimensional phase-contrast magnetic resonance and image-based computational fluid dynamics

OBJECTIVE

This study aims to compare an electrocardiogram (ECG)-gated four-dimensional (4D) phase-contrast (PC) magnetic resonance imaging (MRI) technique and computational fluid dynamics (CFD) using variables controlled in a laboratory environment to minimize bias factors.

MATERIALS AND METHODS

Data from 4D PC-MRI were compared with computational fluid dynamics using steady and pulsatile flows at various inlet velocities. Anatomically realistic models for a normal aorta, a penetrating atherosclerotic ulcer, and an abdominal aortic aneurysm were constructed using a three-dimensional printer.

RESULTS

For the normal aorta model, the errors in the peak and the average velocities were within 5%. The peak velocities of the penetrating atherosclerotic ulcer and the abdominal aortic aneurysm models displayed a more extensive range of differences because of the high-speed and vortical fluid flows generated by the shape of the blood vessel. However, the average velocities revealed only relatively minor differences.

CONCLUSIONS

This study compared the characteristics of PC-MRI and CFD through a phantom study that only included controllable experimental parameters. Based on these results, 4D PC-MRI and CFD are powerful tools for analyzing blood flow patterns in vivo. However, there is room for future developments to improve velocity measurement accuracy.

Index of microcirculatory resistance: state-of-the-art and potential applications in computational simulation of coronary artery disease

The dysfunction of coronary microcirculation is an important cause of coronary artery disease (CAD). The index of microcirculatory resistance (IMR) is a quantitative evaluation of coronary microcirculatory function, which provides a significant reference for the prediction, diagnosis, treatment, and prognosis of CAD. IMR also plays a key role in investigating the interaction between epicardial and microcirculatory dysfunctions, and is closely associated with coronary hemodynamic parameters such as flow rate, distal coronary pressure, and aortic pressure, which have been widely applied in computational studies of CAD. However, there is currently a lack of consensus across studies on the normal and pathological ranges of IMR. The relationships between IMR and coronary hemodynamic parameters have not been accurately quantified, which limits the application of IMR in computational CAD studies. In this paper, we discuss the research gaps between IMR and its potential applications in the computational simulation of CAD. Computational simulation based on the combination of IMR and other hemodynamic parameters is a promising technology to improve the diagnosis and guide clinical trials of CAD.

Patient-Specific Modelling and Parameter Optimisation to Simulate Dilated Cardiomyopathy in Children

PURPOSE

Lumped parameter modelling has been widely used to simulate cardiac function and physiological scenarios in cardiovascular research. Whereas several patient-specific lumped parameter models have been reported for adults, there is a limited number of studies aiming to simulate cardiac function in children. The aim of this study is to simulate patient-specific cardiovascular dynamics in children diagnosed with dilated cardiomyopathy, using a lumped parameter model.

METHODS

Patient data including age, gender, heart rate, left and right ventricular end-systolic and end-diastolic volumes, cardiac output, systolic and diastolic aortic pressures were collected from 3 patients at Great Ormond Street Hospital for Children, London, UK. Ventricular geometrical data were additionally retrieved from cardiovascular magnetic resonance images. 23 parameters in the lumped parameter model were optimised to simulate systolic and diastolic pressures, end-systolic and end-diastolic volumes, cardiac output and left and right ventricular diameters in the patients using a direct search optimisation method.

RESULTS

Difference between the haemodynamic parameters in the optimised cardiovascular system models and clinical data was less than 10%.

CONCLUSION

The simulation results show the potential of patient-specific lumped parameter modelling to simulate clinical cases. Modelling patient specific cardiac function and blood flow in the paediatric patients would allow us to evaluate a variety of physiological scenarios and treatment options.

Applications of computational fluid dynamics to congenital heart diseases: a practical review for cardiovascular professionals

INTRODUCTION

The increased survival rate of patients with congenital heart disease (CHD) has made it likely that 70%-95% of infants with CHDs surviving into adulthood often require careful follow-up and (repeat) interventions. Patients with CHDs often have abnormal blood flow patterns, due to both primary cardiac defect and the consequent surgical or endovascular repair.

AREA COVERED

Computational fluid dynamics (CFD) alone or coupled with advanced imaging tools can assess blood flow patterns of CHDs to both understand their pathophysiology and anticipate the results of surgical or interventional repair.

EXPERT OPINION

CFD is a mathematical technique that quantifies and describes the characteristics of fluid flow using the laws of physics. Through dedicated software based on virtual reconstruction and simulation and patients' real data coming from computed tomography, magnetic resonance imaging, and 3/4 D-ultrasound, reconstruction of models of circulation of most CHD can be accomplished. CFD can provide insights about the pathophysiology of coronary artery anomalies, interatrial shunts, coarctation of the aorta and aortic bicuspid valve, tetralogy of Fallot and univentricular heart, with the capability in some cases of simulating different types of surgical or interventional repair and tailoring the treatment on the basis of these findings.

Characterization of Flow Dynamics in the Pulmonary Bifurcation of Patients With Repaired Tetralogy of Fallot: A Computational Approach

The hemodynamic environment of the pulmonary bifurcation is of great importance for adult patients with repaired tetralogy of Fallot (rTOF) due to possible complications in the pulmonary valve and narrowing of the left pulmonary artery (LPA). The aim of this study was to computationally investigate the effect of geometrical variability and flow split on blood flow characteristics in the pulmonary trunk of patient-specific models. Data from a cohort of seven patients was used retrospectively and the pulmonary hemodynamics was investigated using averaged and MRI-derived patient-specific boundary conditions on the individualized models, as well as a statistical mean geometry. Geometrical analysis showed that curvature and tortuosity are higher in the LPA branch, compared to the right pulmonary artery (RPA), resulting in complex flow patterns in the LPA. The computational analysis also demonstrated high time-averaged wall shear stress (TAWSS) at the outer wall of the LPA and the wall of the RPA proximal to the junction. Similar TAWSS patterns were observed for averaged boundary conditions, except for a significantly modified flow split assigned at the outlets. Overall, this study enhances our understanding about the flow development in the pulmonary bifurcation of rTOF patients and associates some morphological characteristics with hemodynamic parameters, highlighting the importance of patient-specificity in the models. To confirm these findings, further studies are required with a bigger cohort of patients.

Hemodynamic performance of tissue-engineered vascular grafts in Fontan patients

In the field of congenital heart surgery, tissue-engineered vascular grafts (TEVGs) are a promising alternative to traditionally used synthetic grafts. Our group has pioneered the use of TEVGs as a conduit between the inferior vena cava and the pulmonary arteries in the Fontan operation. The natural history of graft remodeling and its effect on hemodynamic performance has not been well characterized. In this study, we provide a detailed analysis of the first U.S. clinical trial evaluating TEVGs in the treatment of congenital heart disease. We show two distinct phases of graft remodeling: an early phase distinguished by rapid changes in graft geometry and a second phase of sustained growth and decreased graft stiffness. Using clinically informed and patient-specific computational fluid dynamics (CFD) simulations, we demonstrate how changes to TEVG geometry, thickness, and stiffness affect patient hemodynamics. We show that metrics of patient hemodynamics remain within normal ranges despite clinically observed levels of graft narrowing. These insights strengthen the continued clinical evaluation of this technology while supporting recent indications that reversible graft narrowing can be well tolerated, thus suggesting caution before intervening clinically.

Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function

In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh-size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms-implemented in the open-source software vmtk-can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.

Computational Analysis of the Pulmonary Arteries in Congenital Heart Disease: A Review of the Methods and Results

With the help of computational fluid dynamics (CFD), hemodynamics of the pulmonary arteries (PA's) can be studied in detail and varying physiological circumstances and treatment options can be simulated. This offers the opportunity to improve the diagnostics and treatment of PA stenosis in biventricular congenital heart disease (CHD). The aim of this review was to evaluate the methods of computational studies for PA's in biventricular CHD and the level of validation of the numerical outcomes. A total of 34 original research papers were selected. The literature showed a great variety in the used methods for (re) construction of the geometry as well as definition of the boundary conditions and numerical setup. There were 10 different methods identified to define inlet boundary conditions and 17 for outlet boundary conditions. A total of nine papers verified their CFD outcomes by comparing results to clinical data or by an experimental mock loop. The diversity in used methods and the low level of validation of the outcomes result in uncertainties regarding the reliability of numerical studies. This limits the current clinical utility of CFD for the study of PA flow in CHD. Standardization and validation of the methods are therefore recommended.

Application of physics-based flow models in cardiovascular medicine: Current practices and challenges

Personalized physics-based flow models are becoming increasingly important in cardiovascular medicine. They are a powerful complement to traditional methods of clinical decision-making and offer a wealth of physiological information beyond conventional anatomic viewing using medical imaging data. These models have been used to identify key hemodynamic biomarkers, such as pressure gradient and wall shear stress, which are associated with determining the functional severity of cardiovascular diseases. Importantly, simulation-driven diagnostics can help researchers understand the complex interplay between geometric and fluid dynamic parameters, which can ultimately improve patient outcomes and treatment planning. The possibility to compute and predict diagnostic variables and hemodynamics biomarkers can therefore play a pivotal role in reducing adverse treatment outcomes and accelerate development of novel strategies for cardiovascular disease management.

Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling

Understanding (patho)physiological phenomena and mechanisms of failure in patients with Fontan circulation-a surgically established circulation for patients born with a functionally single ventricle-remains challenging due to the complex hemodynamics and high inter-patient variations in anatomy and function. In this work, we present a biomechanical model of the heart and circulation to augment the diagnostic evaluation of Fontan patients with early-stage heart failure. The proposed framework employs a reduced-order model of heart coupled with a simplified circulation including venous return, creating a closed-loop system. We deploy this framework to augment the information from data obtained during combined cardiac catheterization and magnetic resonance exams (XMR), performed at rest and during dobutamine stress in 9 children with Fontan circulation and 2 biventricular controls. We demonstrate that our modeling framework enables patient-specific investigation of myocardial stiffness, contractility at rest, contractile reserve during stress and changes in vascular resistance. Hereby, the model allows to identify key factors underlying the pathophysiological response to stress in these patients. In addition, the rapid personalization of the model to patient data and fast simulation of cardiac cycles make our framework directly applicable in a clinical workflow. We conclude that the proposed modeling framework is a valuable addition to the current clinical diagnostic XMR exam that helps to explain patient-specific stress hemodynamics and can identify potential mechanisms of failure in patients with Fontan circulation.

Use of 3D rotational angiography to perform computational fluid dynamics and virtual interventions in aortic coarctation

Computational fluid dynamics (CFD) can be used to analyze blood flow and to predict hemodynamic outcomes after interventions for coarctation of the aorta and other cardiovascular diseases. We report the first use of cardiac 3-dimensional rotational angiography for CFD and show not only feasibility but also validation of its hemodynamic computations with catheter-based measurements in three patients.

Three-dimensional rotational angiography in congenital heart disease: Present status and evolving future

Three-dimensional rotational angiography (3D-RA) enables volumetric imaging through rotation of the C-arm of an angiographic system and real-time 3D reconstruction during cardiac catheterization procedures. In the field of congenital heart disease (CHD), 3D-RA has gained considerable traction, owing to its capability for enhanced visualization of spatial relationships in complex cardiac morphologies and real time image guidance in an intricate interventional environment. This review provides an overview of the current applications, strengths, and limitations of 3D-RA acquisition in the management of CHD and potential future directions. In addition, issues of dosimetry, radiation exposure, and optimization strategies will be reviewed. Further implementation of 3D-RA will be driven by patient benefits relative to existing 3D imaging capabilities and fusion techniques balanced against radiation exposure.

Right Ventricular Dissipative Energy Loss Detected by Vector Flow Mapping in Children: Characteristics of Normal Values

OBJECTIVES

The feasible application of vector flow mapping (VFM)-derived right ventricular (RV) energy loss (EL) is lacking. This study was designed to determine reference values of VFM-derived EL within the right ventricle and evaluate potential correlated variables.

METHODS

A total of 90 healthy children were enrolled. Velocity vector fields of the intra-RV outflow tract and pulmonary trunk (OP) and RV blood flow were obtained from the parasternal short-axis view and RV focused apical 4-chamber view, respectively. RV-EL and OP-EL values during diastole and systole were calculated using VFM analysis. The potential relationships between demographic and echocardiographic parameters and the dissipative EL were also identified.

RESULTS

Mean subject age was 8.99 ± 5.35 years. The median (interquartile range) values were 8.82 (5.47-14.30) W/m for RV diastolic EL, 3.17 (2.11-5.54) W/m for RV systolic EL, 18.82 (13.93-24.92) W/m for OP diastolic EL, and 29.88 (20.62-40.78) W/m for OP systolic EL, respectively. The dissipative EL values were negatively correlated with age and RV global strain, and positively correlated with heart rate and RV Tei index. Multivariate analysis showed that age was the primary independent predictor of these 4 types of EL, while heart rate and strain were contributors of the RV diastolic EL and OP systolic EL.

CONCLUSIONS

The present study initially validated the application of vector flow mapping-derived EL analysis in right ventricle and established reference values for the future assessment of children with cardiopulmonary disease. Age, heart rate, and strain were independent variables correlated with the dissipative EL.

Evaluation of pulmonary artery stenosis in congenital heart disease patients using functional diagnostic parameters: An in vitro study

Congenital pulmonary artery (PA) stenosis is often associated with abnormal PA hemodynamics including increased pressure drop (Δp) and reduced asymmetric flow (Q), which may result in right ventricular dysfunction. We propose functional diagnostic parameters, pressure drop coefficient (CDP), energy loss (E_loss), and normalized energy loss (E¯_loss) to characterize pulmonary hemodynamics, and evaluate their efficacy in delineating stenosis severity using in vitro experiments. Subject-specific test sections including the main PA (MPA) bifurcating into left and right PAs (LPA, RPA) with a discrete LPA stenosis were manufactured from cross-sectional imaging and 3D printing. Three clinically-relevant stenosis severities, 90% area stenosis (AS), 80% AS, and 70% AS, were evaluated at different cardiac outputs (COs). A benchtop flow loop simulating pulmonary hemodynamics was used to measure Q and Δp within the test sections. The experimental Δp-Q characteristics along with clinical data were used to obtain pathophysiologic conditions and compute the diagnostic parameters. The pathophysiologic Q_LPA decreased as the stenosis severity increased at a fixed CO. CDP_LPA, E_loss,LPA (absolute), and E¯_loss,LPA (absolute) increased with an increase in LPA stenosis severity at a fixed CO. Importantly, CDP_LPA and E¯_loss,LPA had reduced variability with CO, and distinct values for each LPA stenosis severity. Under variable CO, a) CDP_LPA values were 14.5-21.0 (70% AS), 60.7- 2.2 (80% AS), ≥ 261.6 (90% AS), and b) E¯_loss,LPA values (in mJ per Q_LPA) were -501.9 to -1023.8 (70% AS), -1247.6 to -1773.0 (80% AS), -1934.5 (90% AS). Hence, CDP_LPA and E¯_loss,LPA are expected to assess the true functional severity of PA stenosis.

Virtual medicine: Utilization of the advanced cardiac imaging patient avatar for procedural planning and facilitation

Advances in imaging technology have led to a paradigm shift from planning of cardiovascular procedures and surgeries requiring the actual patient in a "brick and mortar" hospital to utilization of the digitalized patient in the virtual hospital. Cardiovascular computed tomographic angiography (CCTA) and cardiovascular magnetic resonance (CMR) digitalized 3-D patient representation of individual patient anatomy and physiology serves as an avatar allowing for virtual delineation of the most optimal approaches to cardiovascular procedures and surgeries prior to actual hospitalization. Pre-hospitalization reconstruction and analysis of anatomy and pathophysiology previously only accessible during the actual procedure could potentially limit the intrinsic risks related to time in the operating room, cardiac procedural laboratory and overall hospital environment. Although applications are specific to areas of cardiovascular specialty focus, there are unifying themes related to the utilization of technologies. The virtual patient avatar computer can also be used for procedural planning, computational modeling of anatomy, simulation of predicted therapeutic result, printing of 3-D models, and augmentation of real time procedural performance. Examples of the above techniques are at various stages of development for application to the spectrum of cardiovascular disease processes, including percutaneous, surgical and hybrid minimally invasive interventions. A multidisciplinary approach within medicine and engineering is necessary for creation of robust algorithms for maximal utilization of the virtual patient avatar in the digital medical center. Utilization of the virtual advanced cardiac imaging patient avatar will play an important role in the virtual health care system. Although there has been a rapid proliferation of early data, advanced imaging applications require further assessment and validation of accuracy, reproducibility, standardization, safety, efficacy, quality, cost effectiveness, and overall value to medical care.

Tetralogy of Fallot Surgical Repair: Shunt Configurations, Ductus Arteriosus and the Circle of Willis

In this study, hemodynamic performance of three novel shunt configurations that are considered for the surgical repair of tetralogy of Fallot (TOF) disease are investigated in detail. Clinical experience suggests that the shunt location, connecting angle, and its diameter can influence the post-operative physiology and the neurodevelopment of the neonatal patient. An experimentally validated second order computational fluid dynamics (CFD) solver and a parametric neonatal diseased great artery model that incorporates the ductus arteriosus (DA) and the full patient-specific circle of Willis (CoW) are employed. Standard truncated resistance CFD boundary conditions are compared with the full cerebral arterial system, which resulted 21, -13, and 37% difference in flow rate at the brachiocephalic, left carotid, and subclavian arteries, respectively. Flow splits at the aortic arch and cerebral arteries are calculated and found to change with shunt configuration significantly for TOF disease. The central direct shunt (direct shunt) has pulmonary flow 5% higher than central oblique shunt (oblique shunt) and 23% higher than modified Blalock Taussig shunt (RPA shunt) while the DA is closed. Maximum wall shear stress (WSS) in the direct shunt configuration is 9 and 60% higher than that of the oblique and RPA shunts, respectively. Patent DA, significantly eliminated the pulmonary flow control function of the shunt repair. These results suggests that, due to the higher flow rates at the pulmonary arteries, the direct shunt, rather than the central oblique, or right pulmonary artery shunts could be preferred by the surgeon. This extended model introduced new hemodynamic performance indices for the cerebral circulation that can correlate with the post-operative neurodevelopment quality of the patient.

Vessel tree tracking in angiographic sequences

We present a method to track vessels in angiography [contrast filled vessels in two-dimensional (2-D) x-ray fluoroscopy]. Finding correspondence of a vessel tree from consecutive angiogram frames provides significant value in computer-aided clinical applications such as fast vessel tree segmentation, three-dimensional (3-D) vessel topology reconstruction from corresponding centerlines, cardiac motion understanding, etc. However, establishing an accurate vessel tree correspondence (vessel tree tracking) is a nontrivial problem due to nonlinear periodic cardiac and breathing motion in 2-D views, foreshortening, false bifurcations due to 3-D to 2-D projection, occlusion from other anatomies, etc. The vessel tree is represented by BSpline curves. The control points of the BSpline curves are landmarks that are the tracking targets. Our method maximizes the appearance similarity while preserving the vessel structure. A directed acyclic graph (DAG) is employed to represent the appearance and shape structure of the vessel tree: nodes from the DAG encode the appearance of the vessel tree landmarks, and the edges encode the relative locations between landmarks. The vessel tree tracking problem turns into finding the most similar tree from the DAG in the next frame, and it is solved using an efficient dynamic programming algorithm. We performed evaluations on 62 x-ray angiography sequences (above 1000 frames). Experiment results show our algorithm is robust to these challenges and delivers better performance, compared to four existing methods.

Computational fluid dynamics modelling in cardiovascular medicine

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards ‘digital patient’ or ‘virtual physiological human’ representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Patient-specific assessment of cardiovascular function by combination of clinical data and computational model with applications to patients undergoing Fontan operation

The assessment of cardiovascular function is becoming increasingly important for the care of patients with single-ventricle defects. However, most measurement methods available in the clinical setting cannot provide a separate measure of cardiac function and loading conditions. In the present study, a numerical method has been proposed to compensate for the limitations of clinical measurements. The main idea was to estimate the parameters of a cardiovascular model by fitting model simulations to patient-specific clinical data via parameter optimization. Several strategies have been taken to establish a well-posed parameter optimization problem, including clinical data-matched model development, parameter selection based on an extensive sensitivity analysis, and proper choice of parameter optimization algorithm. The numerical experiments confirmed the ability of the proposed parameter optimization method to uniquely determine the model parameters given an arbitrary set of clinical data. The method was further tested in four patients undergoing the Fontan operation. Obtained results revealed a prevalence of ventricular abnormalities in the patient cohort and at the same time demonstrated the presence of marked inter-patient differences and preoperative to postoperative changes in cardiovascular function. Because the method allows a quick assessment and makes use of clinical data available in clinical practice, its clinical application is promising.

Hemodynamic performance of the Fontan circulation compared with a normal biventricular circulation: a computational model study

The physiological limitations of the Fontan circulation have been extensively addressed in the literature. Many studies emphasized the importance of pulmonary vascular resistance in determining cardiac output (CO) but gave little attention to other cardiovascular properties that may play considerable roles as well. The present study was aimed to systemically investigate the effects of various cardiovascular properties on clinically relevant hemodynamic variables (e.g., CO and central venous pressure). To this aim, a computational modeling method was employed. The constructed models provided a useful tool for quantifying the hemodynamic effects of any cardiovascular property of interest by varying the corresponding model parameters in model-based simulations. Herein, the Fontan circulation was studied compared with a normal biventricular circulation so as to highlight the unique characteristics of the Fontan circulation. Based on a series of numerical experiments, it was found that 1) pulmonary vascular resistance, ventricular diastolic function, and systemic vascular compliance play a major role, while heart rate, ventricular contractility, and systemic vascular resistance play a secondary role in the regulation of CO in the Fontan circulation; 2) CO is nonlinearly related to any single cardiovascular property, with their relationship being simultaneously influenced by other cardiovascular properties; and 3) the stability of central venous pressure is significantly reduced in the Fontan circulation. The findings suggest that the hemodynamic performance of the Fontan circulation is codetermined by various cardiovascular properties and hence a full understanding of patient-specific cardiovascular conditions is necessary to optimize the treatment of Fontan patients.

A computational physiology approach to personalized treatment models: the beneficial effects of slow breathing on the human cardiovascular system

Heart rate variability biofeedback intervention involves slow breathing at a rate of ∼6 breaths/min (resonance breathing) to maximize respiratory and baroreflex effects on heart period oscillations. This intervention has wide-ranging clinical benefits and is gaining empirical support as an adjunct therapy for biobehavioral disorders, including asthma and depression. Yet, little is known about the system-level cardiovascular changes that occur during resonance breathing or the extent to which individuals differ in cardiovascular benefit. This study used a computational physiology approach to dynamically model the human cardiovascular system at rest and during resonance breathing. Noninvasive measurements of heart period, beat-to-beat systolic and diastolic blood pressure, and respiration period were obtained from 24 healthy young men and women. A model with respiration as input was parameterized to better understand how the cardiovascular processes that control variability in heart period and blood pressure change from rest to resonance breathing. The cost function used in model calibration corresponded to the difference between the experimental data and model outputs. A good match was observed between the data and model outputs (heart period, blood pressure, and corresponding power spectral densities). Significant improvements in several modeled cardiovascular functions (e.g., blood flow to internal organs, sensitivity of the sympathetic component of the baroreflex, ventricular elastance) were observed during resonance breathing. Individual differences in the magnitude and nature of these dynamic responses suggest that computational physiology may be clinically useful for tailoring heart rate variability biofeedback interventions for the needs of individual patients.

Model-Based Comparison of the Normal and Fontan Circulatory Systems

Background:

Every year, approximately 1,000 Fontan operations are performed in the United States. Transplant-free, 30-year survival is only 50%. Although some performance characteristics may be universal among Fontan survivors, others may be patient specific and tunable; in either case, a quantitatively rigorous understanding of the Fontan circulatory arrangement would facilitate improvements in patient surveillance and management.

Methods:

To create a computational model of a normal two-year-old and a two-year-old patient with hypoplastic left heart syndrome (HLHS) following staged surgical palliations, we extensively modified the lumped parameter model developed by Clark, a multicompartment model of both pulmonary and systemic circulations.

Results:

With appropriately scaled parameter values, we achieved a maximum relative error (against target values for clinically realistic hemodynamic variables for the normal two-year-old) of 2.8% and an average relative error of 0.9%. Employing the model of a Fontan operation, we achieved a maximum relative error of 2.0% and the average relative error of 0.8%.

Conclusions:

Even with >200 model parameters, once we identified an acceptable set of values for the normal, only 12 required modification in order to attain clinically plausible hemodynamics in the HLHS after Fontan. When placed within the broad context of our extensive model, the impact on cardiac output of the resistance of the total cavopulmonary connection is found to be significantly affected by ventricular elastance and to be much lower in the two-year-old than in patients with markedly lower end-diastolic elastance (higher end-diastolic compliance).