Patient-specific closed-loop model of the fontan circulation: Calibration and validation

The Fontan circulation, designed for managing patients with a single functional ventricle, presents challenges in long-term outcomes. Computational methods offer potential solutions, yet their application in cardiology practice remains largely unexplored. Our aim was to assess the ability of a patient-specific, closed-loop, reduced-order blood flow model to simulate pulsatile blood flow in the Fontan circulation. Using one-dimensional models, we simulated the aorta, superior and inferior venae cavae, and right and left pulmonary arteries, while lumping heart chambers and remaining vessels into zero-dimensional models. The model was calibrated with patient-specific haemodynamic data from combined cardiac catheterisation and magnetic resonance exams, using a novel physics-based stepwise methodology involving simpler open-loop models. Testing on a 10-year-old, anesthetised patient, demonstrated the model's capability to replicate pulsatile pressure and flow in the larger vessels and ventricular pressure. Average relative errors in mean pressure and flow were 2.9 % and 3.6 %, with average relative point-to-point errors (RPPE) in pressure and flow at 5.2 % and 16.0 %. Comparing simulation results to measurements, mean aortic pressure and flow values were 50.7 vs. 50.4 mmHg and 41.6 vs. 41.9 ml/s, respectively, while ventricular pressure values were 28.7 vs. 27.4 mmHg. The model accurately described time-varying ventricular volume with a RPPE of 2.9 %, with mean, minimum, and maximum ventricular volume values for simulation results vs. measurements at 59.2 vs. 58.2 ml, 38.0 vs. 37.6 ml, and 76.0 vs. 74.4 ml, respectively. It provided physiologically realistic predictions of haemodynamic changes from pulmonary vasodilation and atrial fenestration opening. The new model and calibration methodology are freely available, offering a platform to virtually investigate the Fontan circulation's response to clinical interventions and explore potential mechanisms of Fontan failure. Future efforts will concentrate on broadening the model's applicability to a wider range of patient populations and clinical scenarios, as well as testing its effectiveness.

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.

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.

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.

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 Method for In Vitro TCPC Compliance Verification

The Fontan procedure is a common palliative intervention for sufferers of single ventricle congenital heart defects that results in an anastomosis of the venous return to the pulmonary arteries called the total cavopulmonary connection (TCPC). Local TCPC and global Fontan circulation hemodynamics are studied with in vitro circulatory models because of hemodynamic ties to Fontan patient long-term complications. The majority of in vitro studies, to date, employ a rigid TCPC model. Recently, a few studies have incorporated flexible TCPC models, but provide no justification for the model material properties. The method set forth in this study successfully utilizes patient-specific flow and pressure data from phase contrast magnetic resonance images (PCMRI) (n = 1) and retrospective pulse-pressure data from an age-matched patient cohort (n = 10) to verify the compliance of an in vitro TCPC model. These data were analyzed, and the target compliance was determined as 1.36 ± 0.78 mL/mm Hg. A method of in vitro compliance testing and computational simulations was employed to determine the in vitro flexible TCPC model material properties and then use those material properties to estimate the wall thickness necessary to match the patient-specific target compliance. The resulting in vitro TCPC model compliance was 1.37 ± 0.1 mL/mm Hg—a value within 1% of the patient-specific compliance. The presented method is useful to verify in vitro model accuracy of patient-specific TCPC compliance and thus improve patient-specific hemodynamic modeling.

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.

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

Background:

In the absence of an accessible chronic animal model of the Fontan circulation, computational modeling can provide insights into this unique circulatory arrangement, especially how differently it behaves from the normal mammalian circulation. Many groups have focused on refining a single element of the entire Fontan circulation—the total cavopulmonary connection (TCPC). Yet, only modest improvements in transplant-free survival have resulted. From an engineering perspective, optimizing the performance of a complex, multiparameter system requires an understanding of how the performance is affected by the full set of system parameters.

Methods:

We evaluated the hemodynamic impact of nine physiological perturbations in the two-year-old (yo) patient with hypoplastic left heart syndrome having a Fontan rearrangement (using our previously described lumped-parameter multicompartment model of both pulmonary and systemic circulations). In cases where comparison is appropriate, we evaluated the hemodynamic impact of analogous pathophysiologies in the normal two-year-olds. We operated the model in open-loop mode in order to expose the magnitude of the impact of uncompensated physiological perturbations.

Results:

Without the benefit of compensatory mechanisms, a valvar regurgitant fraction of 50% is sufficient to drop the cardiac index (CI) to 2.0 L/min/m2 or less. Aortopulmonary collateral flow of 0.6 L/min (1.1 L/min/m2) or 0.5 L/min (0.9 L/min/m2), sufficient to raise the ratio of pulmonary flow to systemic flow (Qp/Qs) to no higher than 1.2 or 1.5 (fenestration present or absent, respectively), is the maximum which could be tolerated (CI = 2.0 L/min/m2) without the help of compensatory mechanisms. Ventricular end-diastolic elastance (stiffness) changes have dramatic effects on CI in a Fontan circulatory arrangement.

Conclusions:

Several components of the Fontan circulation other than the TCPC actually have equal, or greater, impact on CI under certain conditions.