Introduction

In patients with Fontan palliation, the cardiovascular system is adapting to having systemic arterial, venous, and pulmonary circulations placed in series and connected to a single ventricular pump¹. Such non-physiologically structural characteristics place a burden on a single-ventricle function¹. In addition, the efficiency of flow dynamics within a total cavopulmonary connection (TCPC) can be compromised due to the flow collision from the superior and inferior vena cava (SVC and IVC, respectively) and, potentially, by conduit narrowing. The aim of this study was to quantify the link between the contractile function of a single-ventricle and the fluid dynamic efficiency. Myocardial contractility was estimated by biomechanical modelling of cardiac contraction, and flow energy loss (EL) was quantified from interventional cardiovascular MR (iCMR).

Methods

Data: The study included hemodynamic datasets of 11 patients with hypoplastic left heart syndrome referred for iCMR post-Fontan procedure. Data was collected in the magnet (n=5) or in the catheterization laboratory under the same anesthetic. The study cohort included 9 patients with extracardiac TCPCs and 2 with lateral tunnels, and 8 patients had a fenestration. A highly accelerated prospectively ECG-triggered cine bSSFP sequence was used (kt-SENSE factor 6, partial-Fourier 0.625, slice-thickness 10 mm, special resolution 2.4). Phase contrast flow provided volume flow rate and associated vessel cross-sectional areas in right and left pulmonary arteries (RPA and LPA, respectively), IVC, and SVC (Figure 1). Fontan conduit measurements were obtained by a double-oblique measurement technique using 3D whole-heart inversion recovery b-SSFP images (1.6 to 1.8 mm³ isotropic acquisition). Fenestration flow was clinically defined as the difference between inlet flow (IVC + SVC) and outlet flow (RPA + LPA).

Biophysical model of the heart: The model represented the mechanical (contractile and viscoelastic) behavior of a single ventricular cavity^{2, 3}. Cavity mass and radius were prescribed from the patient’s MRI data. Mechanical laws were calibrated so that simulated waveforms corresponded to the measured maximum and minimum traces for a given patient. The circulation system was represented by a Windkessel model (Figure 2). Calibration of the model to patients' data provided a patient-specific value of myocardial contractility -- i.e., a level of inotropic stress developed by the myocardium during ventricular systole (Figure 3). Maximum time derivative of ventricular pressure (max(dP/dt)) was also computed from model-derived pressure waveforms.

Energy Loss Calculation: EL in the conduit was calculated as in Honda et al.⁴ by taking a difference between inlet and outlet flow energies:
$$EL = \sum Q_i \left( P_i + \frac{1}{2} ρ v_i^2 \right) - \sum Q_o \left( P_o + \frac{1}{2} ρ v_o^2 \right) $$
where, P is pressure (Pa), $$$ρ$$$ is the blood density (1060 kg/m³), Q is the volume flow rate (m³/s), and v is the velocity (m/s). The subscripts ‘i’ and ‘o’ refer to the inlets (IVC and SVC) and outlets (RPA and LPA), respectively. Velocity (v) was obtained by dividing phase contrast flow rate (Q) by the cross-sectional area of a corresponding vessel lumens. The total EL was normalized by the inlet flow energy:
$$EL = \frac{EL_{total}}{\text{Inlet Energy}}$$
All EL calculations were performed in MATLAB (MathWorks, Natick, MA).

Statistical Analysis: Linear regression analysis was performed in R (v4.2.2., R Core Team 2021) between the EL and model-derived myocardial contractility, max(dP/dt), fenestration flow, and minimum conduit area (MCA).

Results

The linear regression analysis revealed that EL was significantly predictive of contractility (R²=0.45, p=0.025) (Figure 4A). The model demonstrated better fit when the Myocardial Mass to End Diastolic Volume (M-to-V) ratio was added as a predictor of contractility in a multivariate regression model (R²=0.94, p<0.001). EL also significantly predicted max(dP/dt) (R²=0.41, p=0.035) (Figure 4B). Finally, fenestration flow was significantly associated with EL (R²=0.52, p=0.012) (Figure 4C). Although mean conduit narrowing was 37.5%, no significant correlation was found between EL and MCA (p=0.246).

Discussion

This study demonstrated the relationship between EL within the Fontan circulation and myocardial contractility metrics. The strong correlation of EL with both contractility and max(dP/dt) suggests a potential role between the ventricular performance and the hemodynamic profile of TCPC. Future research should aim to validate these findings in a larger cohort and assess the long-term clinical impact of the biomechanical factors identified as significant predictors of energy efficiency in Fontan circulation and its link to a long-term myocardial health.

Conclusion

This study reinforces the utility of integrating patient-specific biomechanical modelling with clinical cardiac MRI and hemodynamic data. This integrative approach facilitates a deeper understanding of the complex interactions within the single-ventricle physiology and, when validated, provides a quantitative framework for assessing the efficacy of interventions aimed at improving cardiovascular health of patients with Fontan circulation.

Acknowledgements

The authors would like to acknowledge Dr Philippe Moireau and Dr Dominique Chapelle, Inria, France, research team MΞDISIM, for the development of the cardiac simulation software CardiacLab used in this work.