Conference Agenda

Patient-specific cardiac simulations require the calibration of physical model parameters from measurements of the patient's physiology. Parameter estimation in the heart has been conducted so far using measurements in the myocardium, typically displacement surrogates obtained from MRI. To the best of the authors' knowledge, parameter estimation in cardiac mechanics using velocity images of the ventricular blood flow has remained unexplored. This study assesses the use of Eulerian volumetric velocity images of the ventricular blood flow for estimating material properties of a physiological fully-dimensional fluid–structure interaction (FSI) model of the systolic phase of the heart contraction.
The myocardium is modeled as a hyperelastic material using the standard Holzapfel-Ogden constitutive model with an active contribution to the stress, accounting the contraction of the heart. A fractional step scheme is used to simulate the blood flow efficiently, splitting the Navier–Stokes equations governing the fluid into a tentative velocity step and a projection step to be solved for the fluid pressure. Writing the problem in the Arbitrary Lagrange–Eulerian formalism avoids remeshing the deforming fluid domain at every timestep. In the FSI algorithm, the solid and the fluid problems are coupled in a semi-implicit fashion. In particular, the fluid mesh update and the velocity step are carried out explicitly, depending on the solid displacement of the previous timestep. The fluid's projection step is coupled implicitly to the solid problem, which gives rise to a nonlinear problem, solved with a Krylov–Newton method.
The study considers the left and right ventricles extracted from medical images of a patient. Valve dynamics are not included, as the semilunar valves are considered wide open and the atrioventricular valves closed during systole.
Synthetic measurements of both the solid displacement and the fluid velocity are generated by computing a solution of the FSI problem with fixed ground truth parameters, subsampling the solution in time and adding noise at levels typical for medical images.
The cardiac mechanics model parameters estimated from these measurements are (a) the myocardial tissue contractility, controlling the active contraction, and (b) the epicardial stiffness, characterizing the epicardial wall boundary condition by accounting for the external tissue support. Sequential data assimilation, namely a reduced-order unscented Kalman filter, is employed to estimate the parameters from (i) solid displacement measurements only, (ii) fluid velocity measurements only, or (iii) a combination of both.
Our findings indicate that the accuracy of the estimated parameters with respect to the ground truth strongly depends on the temporal resolution of the data, with only high resolution data allowing for accurate parameter estimates. Using combined fluid and solid measurements reduces the sensitivity of the estimation to measurement noise. The contractility estimation result is closest to the ground truth when using fluid measurements only, whereas the epicardial stiffness is recovered more accurately when using only solid measurements.

Accurate estimation of electrophysiological parameters is crucial for understanding and modeling the dynamic behavior of cardiac tissues across the cardiac cycle, which includes phases of depolarization, repolarization, and refractory periods. These phases underpin the generation and propagation of action potentials that coordinate rhythmic contractions of the heart. In this study, we propose a robust parameter estimation framework based on Differential Evolution (DE) to infer hidden parameters of nonlinear cardiac models. DE, a population-based global optimization algorithm, is particularly suited for handling the nonlinearity and high dimensionality inherent in biological systems. We first demonstrate the effectiveness of DE using the Van der Pol oscillator, a simplified excitable system that mimics the cyclical behavior of cardiac cells. Building on this foundation, we apply our method to more detailed and physiologically relevant models, including the FitzHugh-Nagumo model, which captures essential features of excitability and recovery in cardiac membranes, and the O'Hara-Rudy (ORd) model, which represents detailed ion channel kinetics, intracellular calcium handling, and membrane potential dynamics in human ventricular myocytes. These models are critical for simulating normal and pathological conditions such as early afterdepolarizations, arrhythmias, and conduction blocks. Our results show that DE can accurately recover key parameters even in the presence of sparse or noisy measurements. This highlights DE's value as a powerful tool for inverse modeling in computational cardiology, enabling deeper insight into the mechanisms of cardiac excitability, arrhythmogenesis, and potential therapeutic interventions.

Patient-specific computational models of the cardiovascular system can inform clinical decision-making by providing physics-based, non-invasive calculations of quantities that can not be measured or are impractical to measure and by predicting physiological changes due to interventions.

In particular, mixed-dimensional 3D-0D coupled models can represent spatially resolved 3D myocardial tissue mechanics and 0D pressure-flow relationships in heart valves and vascular system compartments, while accounting for their interactions in a closed-loop setting. They require significantly less computational effort than fully spatially resolved 3D fluid dynamics modeling, which is not required for the considered clinical application.

We present an inverse analysis framework for the automated identification of a set of 3D and 0D patient-specific parameters based on flow, pressure, and cine cardiac MRI measurements. We propose a novel decomposition of the underlying large, nonlinear, and mixed-dimensional inverse problem into an equivalent set of independently solvable, computationally efficient, and well-posed inverse subproblems. This decomposition is enabled by the availability of measurement data of the coupling quantities and ensures a faster convergence towards a unique minimum. For example, if measurements of the right ventricular and pulmonary arterial pressures and pulmonary flow are available, then the parameters of the pulmonary valve submodel can be identified in a completely decoupled manner from neighboring submodels. It avoids the propagation of identification errors, given that submodels do not rely on computed coupling quantities from neighboring submodels to evaluate their response. With the proposed decomposition, we formulate simple and interpretable objective functions and avoid the convergence of the inverse problem to local minima, which do not satisfy all required similarities between computed and measured target quantities. The inverse subproblems are solved with a L-BFGS optimization algorithm and an adjoint gradient evaluation.

The proposed framework is demonstrated in a clinical case study of an adult repaired Tetralogy of Fallot (ToF) patient with severe pulmonary regurgitation. The identified parameters provide a good agreement between measured and computed flows, pressures, and chamber volumes, ensuring a patient-specific model response. The outcome prediction of an in silico pulmonary valve replacement using the personalized model is physiologically consistent and correlates well with postoperative measurements. To successfully implement the proposed approach, detecting, correcting, or removing inaccurate or inconsistent measurements with the guidance of experienced clinicians is required.

The proposed framework is essential for developing accurate and reliable cardiovascular digital twins and exploiting their predictive capabilities for intervention planning.