A simulation protocol for exercise physiology in Fontan patients using a closed loop lumped-parameter model

Predicting the effects of surgically determined parameters on exercise tolerance in Fontan patients

The Fontan physiology is a surgically created circulation for patients with a single functioning ventricle. Patients with this circulation tend to have lower exercise tolerance compared to those with a normal circulation. Important computational and experimental work has been done to investigate this reduction in exercise tolerance. However, there are few systematic modeling studies that focus on the effect of several surgically determined parameters within the same framework. We propose a mathematical model to describe the Fontan circulation under exercise. We then formulate a heuristic based on clinical data from Fontan patients to estimate exercise tolerance. The model is used to investigate the effect of three important surgically determined parameters on exercise tolerance: the systemic arterial compliance, the systemic-venous to pulmonary-venous fenestration, and the resistance of the total cavopulmonary connection.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Switching the Left and the Right Hearts: A Novel Bi-ventricle Mechanical Support Strategy with Spared Native Single-Ventricle

End-stage Fontan patients with single-ventricle (SV) circulation are often bridged-to-heart transplantation via mechanical circulatory support (MCS). Donor shortage and complexity of the SV physiology demand innovative MCS. In this paper, an out-of-the-box circulation concept, in which the left and right ventricles are switched with each other is introduced as a novel bi-ventricle MCS configuration for the "failing" Fontan patients. In the proposed configuration, the systemic circulation is maintained through a conventional mechanical ventricle assist device (VAD) while the venous circulation is delegated to the native SV. This approach spares the SV and puts it to a new use at the right-side providing the most-needed venous flow pulsatility to the failed Fontan circulation. To analyze its feasibility and performance, eight SV failure modes have been studied via an established multi-compartmental lumped parameter cardiovascular model (LPM). Here the LPM model is experimentally validated against the corresponding pulsatile mock-up flow loop measurements of a representative 15-year-old Fontan patient employing a clinically-approved VAD (Medtronic-HeartWare). The proposed surgical configuration maintained the healthy cardiac index (3-3.5 l/min/m2) and the normal mean systemic arterial pressure levels. For a failed SV with low ejection fraction (EF = 26%), representing a typical systemic Fontan failure, the proposed configuration enabled a ~ 28 mmHg amplitude in the venous/pulmonary waveforms and a 2 mmHg decrease in the central venous pressure (CVP) together with acceptable mean pulmonary artery pressures (17.5 mmHg). The pulmonary vascular resistance (PVR)-SV failure case provided a ~ 5 mmHg drop in the CVP, with venous/pulmonary pulsatility reaching to ~ 22 mmHg. For the high PVR failure case with a healthy SV (EF = 44%) pulmonary hypertension is likely to occur as expected. While this condition is routinely encountered during the heart transplantation and managed through pulmonary vasodilators a need for precise functional assessment of the spared failed-ventricle is recommended if utilized in the PVR failure mode. Comprehensive in vitro and in silico results encourage this novel concept as a low-cost, more physiological alternative to the conventional bi-ventricle MCS pending animal experiments.

Passive performance evaluation and validation of a viscous impeller pump for subpulmonary fontan circulatory support

Patients with single ventricle defects undergoing the Fontan procedure eventually face Fontan failure. Long-term cavopulmonary assist devices using rotary pump technologies are currently being developed as a subpulmonary power source to prevent and treat Fontan failure. Low hydraulic resistance is a critical safety requirement in the event of pump failure (0 RPM) as a modest 2 mmHg cavopulmonary pressure drop can compromise patient hemodynamics. The goal of this study is therefore to assess the passive performance of a viscous impeller pump (VIP) we are developing for Fontan patients, and validate flow simulations against in-vitro data. Two different blade heights (1.09 mm vs 1.62 mm) and a blank housing model were tested using a mock circulatory loop (MCL) with cardiac output ranging from 3 to 11 L/min. Three-dimensional flow simulations were performed and compared against MCL data. In-silico and MCL results demonstrated a pressure drop of < 2 mmHg at a cardiac output of 7 L/min for both blade heights. There was good agreement between simulation and MCL results for pressure loss (mean difference - 0.23 mmHg 95% CI [0.24-0.71]). Compared to the blank housing model, low wall shear stress area and oscillatory shear index on the pump surface were low, and mean washout times were within 2 s. This study demonstrated the low resistance characteristic of current VIP designs in the failed condition that results in clinically acceptable minimal pressure loss without increased washout time as compared to a blank housing model under normal cardiac output in Fontan patients.

A Protocol for Coupling Volumetrically Dynamic In-Vitro Experiments to Numerical Physiology Simulation for a Hybrid Cardiovascular Model

OBJECTIVE

The Physiology Simulation Coupled Experiment (PSCOPE) is a hybrid modeling framework that enables a physical fluid experiment to operate in the context of a closed-loop computational simulation of cardiovascular physiology. Previous PSCOPE methods coupled rigid experiments to a lumped parameter network (LPN) of physiology but are incompatible with volumetrically dynamic experiments where fluid volume varies periodically. We address this limitation by introducing a method capable of coupling multi-branch and volumetrically dynamic in-vitro experiments to an LPN.

METHODS

Our proposed method utilizes an iterative weighted-averaging algorithm to identify the unique solution waveforms for a given PSCOPE model. We confirm the accuracy of these PSCOPE solutions by integrating mathematical surrogates of in-vitro experiments directly into the LPN to derive reference solutions, which serve as the gold standard to validate the solutions obtained from using our proposed method to couple the same mathematical surrogates to the LPN. Finally, we illustrate a practical application of our PSCOPE method by coupling an in-vitro renal circulation experiment to the LPN.

RESULTS

Compared to the reference solution, the normalized root mean square error of the flow and pressure waveforms were 0.001%∼0.55%, demonstrating the accuracy of the coupling method.

CONCLUSION

We successfully coupled the in-vitro experiment to the LPN, demonstrating the real-world performance within the constraints of sensor and actuation limitations in the physical experiment.

SIGNIFICANCE

This study introduces a PSCOPE method that can be used to investigate medical devices and anatomies that exhibit periodic volume changes, expanding the utility of the hybrid framework.

Parameter inference in a computational model of haemodynamics in pulmonary hypertension

Pulmonary hypertension (PH), defined by a mean pulmonary arterial pressure (mPAP) greater than 20 mmHg, is characterized by increased pulmonary vascular resistance and decreased pulmonary arterial compliance. There are few measurable biomarkers of PH progression, but a conclusive diagnosis of the disease requires invasive right heart catheterization (RHC). Patient-specific cardiovascular systems-level computational models provide a potential non-invasive tool for determining additional indicators of disease severity. Using computational modelling, this study quantifies physiological parameters indicative of disease severity in nine PH patients. The model includes all four heart chambers, the pulmonary and systemic circulations. We consider two sets of calibration data: static (systolic and diastolic values) RHC data and a combination of static and continuous, time-series waveform data. We determine a subset of identifiable parameters for model calibration using sensitivity analyses and multi-start inference and perform posterior uncertainty quantification. Results show that additional waveform data enables accurate calibration of the right atrial reservoir and pump function across the PH cohort. Model outcomes, including stroke work and pulmonary resistance-compliance relations, reflect typical right heart dynamics in PH phenotypes. Lastly, we show that estimated parameters agree with previous, non-modelling studies, supporting this type of analysis in translational PH research.

Passive Performance Evaluation and Validation of a Viscous Impeller Pump for Subpulmonary Fontan Circulatory Support

Patients with single ventricle defects undergoing the Fontan procedure eventually face Fontan failure. Long-term cavopulmonary assist devices using rotary pump technologies are currently being developed as a subpulmonary power source to prevent and treat Fontan failure. Low hydraulic resistance is a critical safety requirement in the event of pump failure (0 RPM) as a modest 2 mmHg cavopulmonary pressure drop can compromise patient hemodynamics. The goal of this study is therefore to assess the passive performance for a viscous impeller pump (VIP) we are developing for Fontan patients, and validate flow simulations against in-vitro data. Two different blade heights (1.09 mm vs 1.62 mm) and a blank housing model were tested using a mock circulatory loop (MCL) with cardiac output ranging from 3 to 11 L/min. Three-dimensional flow simulations were performed and compared against MCL data. In-silico and MCL results demonstrated a clinically insignificant pressure drop of $<$ 2 mmHg at a cardiac output of 7 L/min for both blade heights. There was good agreement between simulation and MCL results for pressure loss (mean difference -0.23 mmHg 95% CI [0.24 -0.71]). Compared to the blank housing model, low wall shear stress area and oscillatory shear index on the pump surface were low, and mean washout times were within 2 seconds. This study demonstrated the low resistance characteristic of current VIP designs in the failed condition that results in clinically acceptable minimal pressure loss with low risk of thrombosis.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

A computational study of aortic reconstruction in single ventricle patients

Patients with hypoplastic left heart syndrome (HLHS) are born with an underdeveloped left heart. They typically receive a sequence of surgeries that result in a single ventricle physiology called the Fontan circulation. While these patients usually survive into early adulthood, they are at risk for medical complications, partially due to their lower than normal cardiac output, which leads to insufficient cerebral and gut perfusion. While clinical imaging data can provide detailed insight into cardiovascular function within the imaged region, it is difficult to use these data for assessing deficiencies in the rest of the body and for deriving blood pressure dynamics. Data from patients used in this paper include three-dimensional, magnetic resonance angiograms (MRA), time-resolved phase contrast cardiac magnetic resonance images (4D-MRI) and sphygmomanometer blood pressure measurements. The 4D-MRI images provide detailed insight into velocity and flow in vessels within the imaged region, but they cannot predict flow in the rest of the body, nor do they provide values of blood pressure. To remedy these limitations, this study combines the MRA, 4D-MRI, and pressure data with 1D fluid dynamics models to predict hemodynamics in the major systemic arteries, including the cerebral and gut vasculature. A specific focus is placed on studying the impact of aortic reconstruction occurring during the first surgery that results in abnormal vessel morphology. To study these effects, we compare simulations for an HLHS patient with simulations for a matched control patient that has double outlet right ventricle (DORV) physiology with a native aorta. Our results show that the HLHS patient has hypertensive pressures in the brain as well as reduced flow to the gut. Wave intensity analysis suggests that the HLHS patient has irregular circulatory function during light upright exercise conditions and that predicted wall shear stresses are lower than normal, suggesting the HLHS patient may have hypertension.

Multiple blood flow surges during intermittent pneumatic compression: The origins and their implications

Intermittent pneumatic compression (IPC) therapy has been used to enhance peripheral blood flow for prevention and rehabilitation of ischemic-related vascular diseases. A novel phenomenon has been reported that multiple blood flow surges appeared in the skin blood flow signal during each compression, but its mechanism has not been fully revealed. This study aimed to gain insights into the origins of these blood flow surges through experiment and biomechanical modeling methods. Foot skin blood flow (SBF) signals of 13 healthy adults (23.8 ± 0.5 yr old, 7 males) and air cuff pressure signals were recorded during IPC. Lumped parameter modeling and wavelet analysis were adopted to investigate the multiple blood flow surges (named as Peak₁, Peak₂ and Peak₃). The results of the simulated Peak₁ and Peak₂ were in good agreements with the experiment results, suggesting that IPC could enhance foot SBF not only by deflation, but also by inflation. Statistical analysis demonstrated that high frequency compression with more frequent occurrence of Peak₁ and Peak₂ lead to significantly higher (Friedman test, p < 0.001) time-averaged SBF enhancement than the traditional mode. In addition, wavelet analysis showed that the major frequency component of the Peak₃ (0.059 Hz) was within the range of the vascular myogenic activity, suggesting a vascular regulation process triggered by intravascular pressure changes. Our study provide new insights into the mechanism of how IPC enhance foot SBF.

Tunable Blood Shunt for Neonates With Complex Congenital Heart Defects

Despite advancements in procedures and patient care, mortality rates for neonatal recipients of the Norwood procedure, a palliation for single ventricle congenital malformations, remain high due to the use of a fixed-diameter blood shunt. In this study, a new geometrically tunable blood shunt was investigated to address limitations of the current treatment paradigm (e.g., Modified Blalock-Taussig Shunt) by allowing for controlled modulation of blood flow through the shunt to accommodate physiological changes due to the patient’s growth. First, mathematical and computational cardiovascular models were established to investigate the hemodynamic requirements of growing neonatal patients with shunts and to inform design criteria for shunt diameter changes. Then, two stages of prototyping were performed to design, build and test responsive hydrogel systems that facilitate tuning of the shunt diameter by adjusting the hydrogel’s degree of crosslinking. We examined two mechanisms to drive crosslinking: infusion of chemical crosslinking agents and near-UV photoinitiation. The growth model showed that 15–18% increases in shunt diameter were required to accommodate growing patients’ increasing blood flow; similarly, the computational models demonstrated that blood flow magnitudes were in agreement with previous reports. These target levels of diameter increases were achieved experimentally with model hydrogel systems. We also verified that the photocrosslinkable hydrogel, composed of methacrylated dextran, was contact-nonhemolytic. These results demonstrate proof-of-concept feasibility and reflect the first steps in the development of this novel blood shunt. A tunable shunt design offers a new methodology to rebalance blood flow in this vulnerable patient population during growth and development.

A Mechanistic Lumped Parameter Model of the Berlin Heart EXCOR to Analyze Device Performance and Physiologic Interactions

PURPOSE

The Berlin Heart EXCOR (BH) is the only FDA-approved, extracorporeal pulsatile ventricular assist device (VAD) for infants and children with heart failure. Clinicians control four settings on the device-systolic and diastolic drive pressures, device pump rate, and systolic time as a percentage of the pump cycle. However, interactions between BH pneumatics and the native circulation remain poorly understood. Thus, establishing appropriate device size and settings can be challenging on a patient-to-patient basis.

METHODS

In this study we develop a novel lumped parameter network based on simplified device mechanics. We perform parametric studies to characterize device behavior, study interactions between the left ventricle (LV) and BH across different device settings, and develop patient-specific simulations. We then simulate the impact of changing device parameters for each of three patients.

RESULTS

Increasing systolic pressure and systolic time increased device output. We identified previously unobserved cycle-to-cycle variations in LV-BH interactions that may impact patient health. Patient-specific simulations demonstrated the model's ability to replicate BH performance, captured trends in LV behavior after device implantation, and emphasized the importance of device rate and volume in optimizing BH efficiency.

CONCLUSION

We present a novel, mechanistic model that can be readily adjusted to study a wide range of device settings and clinical scenarios. Physiologic interactions between the BH and the native LV produced large variability in cardiac loading. Our findings showed that operating the BH at a device rate greater than the patient's native heart decreases variability in physiological interactions between the BH and LV, increasing cardiac offloading while maintaining cardiac output. Device rates that are close to the resting heart rate may result in unfavorable cardiac loading conditions. Our work demonstrates the utility of our model to investigate BH performance for patient-specific physiologies.

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

Parameter estimation for closed-loop lumped parameter models of the systemic circulation using synthetic data

Physics-based models can be applied to describe mechanisms in both health and disease, which has the potential to accelerate the development of personalized medicine. The aim of this study was to investigate the feasibility of personalizing a model of systemic hemodynamics by estimating model parameters. We investigated the feasibility of estimating model parameters for a closed-loop lumped parameter model of the left heart and systemic circulation using the step-wise subset reduction method. This proceeded by first investigating the structural identifiability of the model parameters. Secondly we performed sensitivity analysis to determine which parameters were most influential on the most relevant model outputs. Finally, we constructed a sequence of progressively smaller subsets including parameters based on their ranking by model output influence. The model was then optimized to data for each set of parameters to evaluate how well the parameters could be estimated for each subset. The subsequent results allowed assessment of how different data sets, and noise affected the parameter estimates. In the noiseless case, all parameters could be calibrated to less than 10^-3% error using time series data, while errors using clinical index data could reach over 100%. With 5% normally distributed noise the accuracy was limited to be within 10% error for the five most sensitive parameters, while the four least sensitive parameters were unreliably estimated for waveform data. The three least sensitive parameters were particularly challenging to estimate so these should be prioritised for measurement. Cost functions based on time series such as pressure waveforms, were found to give better parameter estimates than cost functions based on standard indices used in clinical assessment of the cardiovascular system, for example stroke volume (SV) and pulse pressure (PP). Averaged parameter estimate errors were reduced by several orders of magnitude by choosing waveforms for noiseless synthetic data. Also when measurement data were noisy, the parameter estimation procedure based on continuous waveforms was more accurate than that based on clinical indices. By application of the step-wise subset reduction method we demonstrated that by the addition of venous pressure to the cost function, or conversely fixing the systemic venous compliance parameter at an accurate value improved all parameter estimates, especially the diastolic filling parameters which have least influence on the aortic pressure.

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.

Engineering Perspective on Cardiovascular Simulations of Fontan Hemodynamics: Where Do We Stand with a Look Towards Clinical Application

BACKGROUND

Cardiovascular simulations for patients with single ventricles undergoing the Fontan procedure can assess patient-specific hemodynamics, explore surgical advances, and develop personalized strategies for surgery and patient care. These simulations have not yet been broadly accepted as a routine clinical tool owing to a number of limitations. Numerous approaches have been explored to seek innovative solutions for improving methodologies and eliminating these limitations.

PURPOSE

This article first reviews the current state of cardiovascular simulations of Fontan hemodynamics. Then, it will discuss the technical progress of Fontan simulations with the emphasis of its clinical impact, noting that substantial improvements have been made in the considerations of patient-specific anatomy, flow, and blood rheology. The article concludes with insights into potential future directions involving clinical validation, uncertainty quantification, and computational efficiency. The advancements in these aspects could promote the clinical usage of Fontan simulations, facilitating its integration into routine clinical practice.

Multiscale modeling of a modified Blalock-Taussig surgery in a patient-specific tetralogy of Fallot

Tetralogy of Fallot (TOF) is a congenital heart anomaly that causes a drastic reduction in the oxygen level. In this study, we coupled a lumped-parameter model with a patient-specific three-dimensional (3D) model which included a modified Blalock-Taussig (MBT) shunt. By forming a closed loop, we investigated the effects of certain parameters on the flow rates and the pressures at different locations of the developed network. A local sensitivity analysis on an initial zero-dimensional (0D) closed-loop model was conducted. The 0D lumped parameter (LP) model was then refined based on the results of the multiscale 0D-3D model and the local sensitivity analysis was repeated for the refined 0D model. It was shown that the maximum pressure of the pulmonary bed had the highest sensitivity of 94% to the diameter of MBT shunt. We observed that the existence of the flow in the shunt during the diastole caused an elevated wall shear stress (WSS) in the pulmonary artery. In this work, we calculated the flow velocity and pressure field in a 3D patient-specific aorta with an MBT shunt, and then we used the results to increase the accuracy of our LP model to simulate numerous 0D simulations in a significantly shorter time, which is potentially applicable for medical decision-making.

Calibration of an Electrical Analog Model of Liver Hemodynamics in Fontan Patients

Fontan associated liver disease is a common complication in patients with Fontan circulation, who were born with a single functioning heart ventricle. The hepatic venous pressure gradient (HVPG) is used to assess liver health and is a surrogate measure of the pressure gradient across the entire liver (portal pressure gradient (PPG)). However, it is thought to be inaccurate in Fontan patients. The main objectives of this study were (1) to apply an existing detailed lumped parameter model (LPM) of the liver to Fontan patients using patient-specific clinical data and (2) to determine whether HVPG is a suitable measurement of PPGs in these patients. An existing LPM of the liver blood circulation was applied and tuned to simulate patient-specific liver hemodynamics. Geometries were collected from seven adult Fontan patients and used to evaluate model parameters. The model was solved and tuned using waveform measurements of flows, inlet and outlet pressures. The predicted ratio of portal to hepatic venous pressures is comparable to in vivo measurements. The results confirmed that HVPG is not suitable for Fontan patients, as it would underestimate the portal pressures gradient by a factor of 3 to 4. Our patient-specific liver model provides an estimate of the pressure drop across the liver, which differs from the clinically used metric HVPG. This work represents a first step toward models suitable to assess liver health in Fontan patients and improve its long-term management.

Target Flow-Pressure Operating Range for Designing a Failing Fontan Cavopulmonary Support Device

Fontan operation as the current standard of care for the palliation of single ventricle defects results in significant late complications. Using a mechanical circulatory device for the right circulation to serve the function of the missing subpulmonary ventricle could potentially stabilize the failing Fontan circulation. This study aims to elucidate the hydraulic operating regions that should be targeted for designing cavopulmonary blood pumps. By integrating numerical analysis and available clinical information, the interaction of the cavopulmonary support via the IVC and full assist configurations with a wide range of simulated adult failing scenarios was investigated; with IVC and full assist corresponding to the inferior venous return or the entire venous return, respectively, being routed through the device. We identified the desired hydraulic operating regions for a cavopulmonary assist device by clustering all head pressures and corresponding pump flows that result in hemodynamic improvement for each simulated failing Fontan physiology. Results show that IVC support can produce beneficial hemodynamics in only a small fraction of failing Fontan scenarios. Cavopulmonary assist device could increase cardiac index by 35% and decrease the inferior vena cava pressure by 45% depending on the patient's pre-support hemodynamic state and surgical configuration of the cavopulmonary assist device (IVC or full support). The desired flow-pressure operating regions we identified can serve as the performance criteria for designing cavopulmonary assist devices as well as evaluating off-label use of commercially available left-side blood pumps for failing Fontan cavopulmonary support.

A patient-specific modelling method of blood circulatory system for the numerical simulation of enhanced external counterpulsation

Lumped parameter model (LPM) is a common numerical model for hemodynamic simulation of human's blood circulatory system. The numerical simulation of enhanced external counterpulsation (EECP) is a typical biomechanical simulation process based on the LPM of blood circulatory system. In order to simulate patient-specific hemodynamic effects of EECP and develop best treatment strategy for each individual, this study developed an optimization algorithm to individualize LPM elements. Physiological data from 30 volunteers including approximate aortic pressure, cardiac output, ankle pressure and carotid artery flow were clinically collected as optimization objectives. A closed-loop LPM was established for the simulation of blood circulatory system. Aiming at clinical data, a sensitivity analysis for each element was conducted to identify the significant ones. We improved the traditional simulated annealing algorithm to iteratively optimize the sensitive elements. To verify the accuracy of the patient-specific model, 30 samples of simulated data were compared with clinical measurements. In addition, an EECP experiment was conducted on a volunteer to verify the applicability of the optimized model for the simulation of EECP. For these 30 samples, the optimization results show a slight difference between clinical data and simulated data. The average relative root mean square error is lower than 5%. For the subject of EECP experiment, the relative error of hemodynamic responses during EECP is lower than 10%. This slight error demonstrated a good state of optimization. The optimized modeling algorithm can effectively individualize the LPM for blood circulatory system, which is significant to the numerical simulation of patient-specific hemodynamics.

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.

Computational Modeling to Support Surgical Decision Making in Single Ventricle Physiology

Many of the advances in congenital heart surgery were built upon lessons and insights gained from model simulations. While animal and mock-circuit models have historically been the main arena to test new operative techniques and concepts, the recognition that complex cardiovascular anatomy and circulation can be modeled mathematically ushered a new era of collaboration between surgeons and engineers. In 1996, the computational age in congenital heart surgery began when investigators in London and Milan tapped the power of the computer to simulate the Fontan procedure and introduced operative improvements. Since then, computational modeling has led to numerous contributions in congenial heart surgery as continuing sophistication and advances in numerical and imaging methods furthered the ability to refine anatomic and physiologic details. Idealized generic models have given way to precise patient-specific simulations of the 3-dimensional anatomy, reconstructed circulation, affected hemodynamics, and altered physiology. Tools to perform virtual surgery, and predict flow dynamic and circulatory results, have been developed for some of the most complex defects, such as those requiring single ventricle palliation. In today's quest for personalized medicine and precision care, computational modeling's role to assist surgical planning in complex congenital heart surgery will continue to grow and evolve. With ever closer collaboration between surgeons and engineers, and clear understanding of modeling limitations, computational simulations can be a valuable adjunct to support preoperative surgical decision making.

An algorithm for coupling multibranch in vitro experiment to numerical physiology simulation for a hybrid cardiovascular model

The hybrid cardiovascular modeling approach integrates an in vitro experiment with a computational lumped-parameter simulation, enabling direct physical testing of medical devices in the context of closed-loop physiology. The interface between the in vitro and computational domains is essential for properly capturing the dynamic interactions of the two. To this end, we developed an iterative algorithm capable of coupling an in vitro experiment containing multiple branches to a lumped-parameter physiology simulation. This algorithm identifies the unique flow waveform solution for each branch of the experiment using an iterative Broyden's approach. For the purpose of algorithm testing, we first used mathematical surrogates to represent the in vitro experiments and demonstrated five scenarios where the in vitro surrogates are coupled to the computational physiology of a Fontan patient. This testing approach allows validation of the coupling result accuracy as the mathematical surrogates can be directly integrated into the computational simulation to obtain the "true solution" of the coupled system. Our algorithm successfully identified the solution flow waveforms in all test scenarios with results matching the true solutions with high accuracy. In all test cases, the number of iterations to achieve the desired convergence criteria was less than 130. To emulate realistic in vitro experiments in which noise contaminates the measurements, we perturbed the surrogate models by adding random noise. The convergence tolerance achievable with the coupling algorithm remained below the magnitudes of the added noise in all cases. Finally, we used this algorithm to couple a physical experiment to the computational physiology model to demonstrate its real-world applicability.

Risks and Benefits of Using a Commercially Available Ventricular Assist Device for Failing Fontan Cavopulmonary Support: A Modeling Investigation

Fontan patients often develop circulatory failure and are in desperate need of a therapeutic solution. A blood pump surgically placed in the cavopulmonary pathway can substitute the function of the absent sub-pulmonary ventricle by generating a mild pressure boost. However, there is currently no commercially available device designed for the cavopulmonary application; and the risks and benefits of implanting a ventricular assist device (VAD), originally designed for the left ventricular application, on the right circulation of failing Fontan patients is not yet clear. Moreover, further research is needed to compare the hemodynamics between the two clinically-considered surgical configurations for cavopulmonary assist, with Full and inferior vena cava (IVC) support corresponding to the entire venous return or only the inferior venous return, respectively, being routed through the VAD. In this study, we used a numerical model of the failing Fontan physiology to evaluate the Fontan hemodynamic response to a left VAD during the IVC and Full support scenarios. We observed that during Full support, the VAD improved the cardiac output while maintaining blood pressures within safe ranges, and lowered the IVC pressure to <15 mmHg; however, we found a potential risk of lung damage at higher pump speeds due to the excessive pulmonary pressure elevation. IVC support, on the other hand, did not benefit the hemodynamics in the patient cases simulated, resulting in the superior vena cava pressure increasing to an unsafe level of >20 mmHg. The findings in this study may be helpful to surgeons for recognizing the risks of a cavopulmonary VAD and developing coherent clinical strategies for the implementation of cavopulmonary support.

Computational Fluid Dynamics of Vascular Disease in Animal Models

Recent applications of computational fluid dynamics (CFD) applied to the cardiovascular system have demonstrated its power in investigating the impact of hemodynamics on disease initiation, progression, and treatment outcomes. Flow metrics such as pressure distributions, wall shear stresses (WSS), and blood velocity profiles can be quantified to provide insight into observed pathologies, assist with surgical planning, or even predict disease progression. While numerous studies have performed simulations on clinical human patient data, it often lacks prediagnosis information and can be subject to large intersubject variability, limiting the generalizability of findings. Thus, animal models are often used to identify and manipulate specific factors contributing to vascular disease because they provide a more controlled environment. In this review, we explore the use of CFD in animal models in recent studies to investigate the initiating mechanisms, progression, and intervention effects of various vascular diseases. The first section provides a brief overview of the CFD theory and tools that are commonly used to study blood flow. The following sections are separated by anatomical region, with the abdominal, thoracic, and cerebral areas specifically highlighted. We discuss the associated benefits and obstacles to performing CFD modeling in each location. Finally, we highlight animal CFD studies focusing on common surgical treatments, including arteriovenous fistulas (AVF) and pulmonary artery grafts. The studies included in this review demonstrate the value of combining CFD with animal imaging and should encourage further research to optimize and expand upon these techniques for the study of vascular disease.

4D Flow MRI Estimation of Boundary Conditions for Patient Specific Cardiovascular Simulation

Accurate image based cardiovascular simulations require patient specific boundary conditions (BCs) for inlets, outlets and vessel wall mechanical properties. While inlet BCs are typically determined non-invasively, invasive pressure catheterization is often used to determine patient specific outlet BCs and vessel wall mechanical properties. A method using 4D Flow MRI to non-invasively determine both patient specific outlet BCs and vessel wall mechanical properties is presented and results for both in vitro validation with a latex tube and an in vivo pulmonary artery stenosis (PAS) stent intervention are presented. For in vitro validation, acceptable agreement is found between simulation using BCs from 4D Flow MRI and benchtop measurements. For the PAS virtual intervention, simulation correctly predicts flow distribution with 9% error compared to MRI. Using 4D Flow MRI to noninvasively determine patient specific BCs increases the ability to use image based simulations as pressure catheterization is not always performed.

A Hybrid Experimental-Computational Modeling Framework for Cardiovascular Device Testing

Significant advances in biomedical science often leverage powerful computational and experimental modeling platforms. We present a framework named physiology simulation coupled experiment ("PSCOPE") that can capitalize on the strengths of both types of platforms in a single hybrid model. PSCOPE uses an iterative method to couple an in vitro mock circuit to a lumped-parameter numerical simulation of physiology, obtaining closed-loop feedback between the two. We first compared the results of Fontan graft obstruction scenarios modeled using both PSCOPE and an established multiscale computational fluid dynamics method; the normalized root-mean-square error values of important physiologic parameters were between 0.1% and 2.1%, confirming the fidelity of the PSCOPE framework. Next, we demonstrate an example application of PSCOPE to model a scenario beyond the current capabilities of multiscale computational methods-the implantation of a Jarvik 2000 blood pump for cavopulmonary support in the single-ventricle circulation; we found that the commercial Jarvik 2000 controller can be modified to produce a suitable rotor speed for augmenting cardiac output by approximately 20% while maintaining blood pressures within safe ranges. The unified modeling framework enables a testing environment which simultaneously operates a medical device and performs computational simulations of the resulting physiology, providing a tool for physically testing medical devices with simulated physiologic feedback.

Fontan Surgical Planning: Previous Accomplishments, Current Challenges, and Future Directions

The ultimate goal of Fontan surgical planning is to provide additional insights into the clinical decision-making process. In its current state, surgical planning offers an accurate hemodynamic assessment of the pre-operative condition, provides anatomical constraints for potential surgical options, and produces decent post-operative predictions if boundary conditions are similar enough between the pre-operative and post-operative states. Moving forward, validation with post-operative data is a necessary step in order to assess the accuracy of surgical planning and determine which methodological improvements are needed. Future efforts to automate the surgical planning process will reduce the individual expertise needed and encourage use in the clinic by clinicians. As post-operative physiologic predictions improve, Fontan surgical planning will become an more effective tool to accurately model patient-specific hemodynamics.

Lumped parameter model for hemodynamic simulation of congenital heart diseases

The recent development of computer technology has made it possible to simulate the hemodynamics of congenital heart diseases on a desktop computer. However, multi-scale modeling of the cardiovascular system based on computed tomographic and magnetic resonance images still requires long simulation times. The lumped parameter model is potentially beneficial for real-time bedside simulation of congenital heart diseases. In this review, we introduce the basics of the lumped parameter model (time-varying elastance chamber model combined with modified Windkessel vasculature model) and illustrate its usage in hemodynamic simulation of congenital heart diseases using examples such as hypoplastic left heart syndrome and Fontan circulation. We also discuss the advantages of the lumped parameter model and the problems for clinical use.

A computational study of the Fontan circulation with fenestration or hepatic vein exclusion

Fontan patients may undergo additional surgical modifications to mitigate complications like protein-losing enteropathy, liver cirrhosis, and other issues in their splanchnic circulation. Recent case reports show promise for several types of modifications, but the subtle effects of these surgeries on the circulation are not well understood. In this paper, we employ mathematical modeling of blood flow to systematically quantify the impact of these surgical changes on extracardiac Fontan hemodynamics. We investigate two modifications: (1) the fenestrated Fontan and (2) the Fontan with hepatic vein exclusion. Closed-loop hemodynamic models are used, which consist of one-dimensional networks for the major vessels and zero-dimensional models for the heart and organ beds. Numerical results suggest the hepatic vein exclusion has the greatest overall impact on the hemodynamics, followed by the largest sized fenestration. In particular, the hepatic vein exclusion drastically lowers portal venous pressure while the fenestration decreases pulmonary artery pressure. Both modifications increase flow to the intestines, a finding consistent with their utility in clinical practice for combating complications in the splanchnic circulation.

Mathematical modelling of the maternal cardiovascular system in the three stages of pregnancy

In this study, a mathematical model of the female circulation during pregnancy is presented in order to investigate the hemodynamic response to the cardiovascular changes associated with each trimester of pregnancy. First, a preliminary lumped parameter model of the circulation of a non-pregnant female was developed, including the heart, the systemic circulation with a specific block for the uterine district and the pulmonary circulation. The model was first tested at rest; then heart rate and vascular resistances were individually varied to verify the correct response to parameter alterations characterising pregnancy. In order to simulate hemodynamics during pregnancy at each trimester, the main changes applied to the model consisted in reducing vascular resistances, and simultaneously increasing heart rate and ventricular wall volumes. Overall, reasonable agreement was found between model outputs and in vivo data, with the trends of the cardiac hemodynamic quantities suggesting correct response of the heart model throughout pregnancy. Results were reported for uterine hemodynamics, with flow tracings resembling typical Doppler velocity waveforms at each stage, including pulsatility indexes. Such a model may be used to explore the changes that happen during pregnancy in female with cardiovascular diseases.

Model-Based Comparison of the Normal and Fontan Circulatory Systems-Part III

BACKGROUND

For patients with the Fontan circulatory arrangement, angiotensin-converting enzyme inhibition, guanylate cyclase activation, phosphodiesterase 5 inhibition, and endothelin receptor antagonism have so far resulted in little or no improvement in [Formula: see text] or peak cardiac index (CI), suggesting that our understanding of the factors that most impact the exercise hemodynamics is incomplete.

METHODS

To facilitate comparisons with clinical reports of the exercise performance of preadolescent Fontan patients, we rescaled our previously reported computational models of a two-year-old normal child and similarly aged Fontan patient, extended our Fontan model to capture the nonlinear relationship between flow and resistance quantified from previous computational fluid dynamic analyses of the total cavopulmonary connection (TCPC), and added respiration as well as skeletal muscle contraction.

RESULTS

(1) Without respiration, the computational model for both the normal and the Fontan cannot attain the values for CI at peak exercise reported in the clinical literature, (2) because flow through the TCPC is much greater during inspiration than during expiration, the effect on the CI of the dynamic (flow-related) TCPC resistance is much more dramatic during exercise than it is in breath-hold mode at rest, and (3) coupling breathing with skeletal muscle contraction leads to the highest augmentation of cardiac output, that is, the skeletal muscle pump is most effective when the intrathoracic pressure is at a minimum-at peak inspiration.

CONCLUSIONS

Novel insights emerge when a Fontan model incorporating dynamic TCPC resistance, full respiration, and skeletal muscle contraction can be compared to the model of the normal.

A Numerical Simulation Comparing a Cavopulmonary Assist Device and VA ECMO for Failing Fontan Support

A cavopulmonary assist device (CPAD) has been developed for failing Fontan support. This CPAD pumps blood from superior/inferior vena cavae (SVC/IVC) to pulmonary artery. In this study, we compared failing Fontan support with CPAD versus veno-arterial extracorporeal membrane oxygenation (VA ECMO) in silico. A numerical lumped-parameter circulatory system model was used to simulate Fontan circulation. Failing Fontan was simulated by increased pulmonary resistance. Central venous pressure (CVP), mean pulmonary arterial pressure (mPAP), left atrial pressure (LAP), and univentricular outflow (CO) were simulated and compared with published clinical data. The CPAD and VA ECMO were simulated using 1-5 L/min pump flows. In agreement with published clinical data, the simulated failing Fontan condition had increased CVP (19 mmHg) and mPAP (18 mmHg) with decreased LAP (7 mmHg) and cardiac output (3 L/min) compared with functional Fontan condition. The CPAD achieved total Fontan assistance with pump flows higher than original CO. Veno-arterial extracorporeal membrane oxygenation provided partial Fontan assistance with low pump flows. Blood went through pulmonary circulation with CPAD whereas VA ECMO bypassed pulmonary circulation and diminished univentricular blood flow (0.8 L/min). This in silico study demonstrated that CPAD preserved heart/lung function whereas VA ECMO had very low univentricular flow, potentially leading to thrombosis or univentricular atrophy.

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 Surgical Planning, Where Do We Stand? The Example of the Fontan Procedure

The Fontan surgery for single ventricle heart defects is a typical example of a clinical intervention in which patient-specific computational modeling can improve patient outcome: with the functional heterogeneity of the presenting patients, which precludes generic solutions, and the clear influence of the surgically-created Fontan connection on hemodynamics, it is acknowledged that individualized computational optimization of the post-operative hemodynamics can be of clinical value. A large body of literature has thus emerged seeking to provide clinically relevant answers and innovative solutions, with an increasing emphasis on patient-specific approaches. In this review we discuss the benefits and challenges of patient-specific simulations for the Fontan surgery, reviewing state of the art solutions and avenues for future development. We first discuss the clinical impact of patient-specific simulations, notably how they have contributed to our understanding of the link between Fontan hemodynamics and patient outcome. This is followed by a survey of methodologies for capturing patient-specific hemodynamics, with an emphasis on the challenges of defining patient-specific boundary conditions and their extension for prediction of post-operative outcome. We conclude with insights into potential future directions, noting that one of the most pressing issues might be the validation of the predictive capabilities of the developed framework.

Computational modeling of pathophysiologic responses to exercise in Fontan patients

Reduced exercise capacity is nearly universal among Fontan patients. Although many factors have emerged as possible contributors, the degree to which each impacts the overall hemodynamics is largely unknown. Computational modeling provides a means to test hypotheses of causes of exercise intolerance via precisely controlled virtual experiments and measurements. We quantified the physiological impacts of commonly encountered, clinically relevant dysfunctions introduced to the exercising Fontan system via a previously developed lumped-parameter model of Fontan exercise. Elevated pulmonary arterial pressure was observed in all cases of dysfunction, correlated with lowered cardiac output (CO), and often mediated by elevated atrial pressure. Pulmonary vascular resistance was not the most significant factor affecting exercise performance as measured by CO. In the absence of other dysfunctions, atrioventricular valve insufficiency alone had significant physiological impact, especially under exercise demands. The impact of isolated dysfunctions can be linearly summed to approximate the combined impact of several dysfunctions occurring in the same system. A single dominant cause of exercise intolerance was not identified, though several hypothesized dysfunctions each led to variable decreases in performance. Computational predictions of performance improvement associated with various interventions should be weighed against procedural risks and potential complications, contributing to improvements in routine patient management protocol.