Fig 1.
Processed data of a selected Fontan patient acquired at rest (left) and during dobutamine stress (right).
Fig 2.
Scheme of the closed-loop heart-circulation model.
The circuit is closed by linear venous return law (blue dashed line in the right panel given by Eq (9)), which defines the venous pressure and preload of systemic ventricle according to the cardiac output (MSFP stands for mean systemic filling pressure and
for maximum achievable venous flow).
Fig 3.
Frank-Starling mechanism and electrical activation Left: Maximum effect of the Frank-Starling mechanism (n0(efib) = 1) at optimal fiber extension. Right: Profile of the electrical activation function u with a rescaled ventricular volume plot. The measured durations of QRS, PQ and ST segments of ECG at rest are used to impose timings for the electrical activation function and for the atrial contraction.
Fig 4.
Calibration of the Windkessel model (left), and of the heart model with prescribed level of preload (right) at rest. For visualization purposes, the aortic flow was downscaled by a factor of 2.
Fig 5.
Example simulation for Fontan patient.
Simulations for FP#1 at rest (black) and during dobutamine stress (blue).
Fig 6.
Example simulation for patient with biventricular heart.
Simulations for CC#1 at rest (black) and during dobutamine stress (blue). Note the significant upward shift of the venous return curve that improves the ability to augment CO during stress.
Fig 7.
Model estimated quantities vs measurements.
Left: Model-derived distal Windkessel resistance (Rd) versus measured vascular resistance at rest. Right: Model estimated contractility versus measured ventricular max dp/dt. Markers • denote FPs, + denote CC#1 and * denote CC#2.
Table 1.
Patients’ characteristics as directly obtained from the data at rest.
Table 2.
Patients’ characteristics obtained by calibrating the patient-specific models at rest.
Table 3.
Summary of the changes in contractility, vascular resistance and venous return in the model for Fontan patients (FP) and control cases (CC) during dobutamine stress.
Fig 8.
Effect of the venous return augmentation.
Cardiac output curves of FP#4 at rest (black) and during dobutamine stress with the cardiac output-venous return equilibrium points of the closed-loop system marked by asterisks—purple for the cardiac output at stress while the venous return kept as at rest, and blue allowing an increase of venous return ( increased by 45%) during dobutamine stress.
Fig 9.
Chronotropic and inotropic effects.
The closed-loop heart-circulation model for FP#1 calibrated at rest (black), the predicted chronotropic effect for heart rate as during dobutamine stress but without the inotropic component (purple). The additional inotropic effect (blue) brings the simulation close to the data (dashed blue line).
Table 4.
Sensitivity analysis for two selected Fontan patients when varying mean systemic filling pressure at rest (MSFP) between 15 and 25 mmHg: No change in the estimated contractility and contractile reserve, and the estimated change of maximum venous return varied by less than 5%.