Conference Agenda

Zero-dimensional (0D) cardiovascular models are widely used to simulate hemodynamics across the entire circulation, supporting applications from clinical decision-making to surgical planning. However, their real power lies in solving inverse problems, where patient-specific parameters are estimated from measurable outputs such as pressures or flow rates. These tasks, parameter estimation and uncertainty quantification (UQ), are computationally intensive, often requiring thousands of model evaluations. In this work, we present a comprehensive metamodeling pipeline that enables fast and reliable inverse problem-solving for 0D cardiovascular systems.

We compare three surrogate modeling approaches—feed-forward neural networks (NNs), polynomial chaos expansion (PCE), and Gaussian processes (GPs)—in their ability to emulate 0D models and support inverse tasks. Surrogates are trained on synthetic datasets generated via Saltelli’s sampling scheme and evaluated across three representative 0D models: (1) portal pressure prediction after liver resection, (2) hemodynamic modeling of pulmonary arterial hypertension (PAH) before and after Potts shunt placement, and (3) contrast-agent transport for perfusion assessment. These cases cover both scalar and time-series outputs, with the latter addressed using LSTM architectures.

Focusing on the PAH model, we demonstrate the full inverse pipeline using a trained NN surrogate. First, we perform variance-based sensitivity analysis using Monte Carlo Sobol indices to identify the most influential parameters. These insights guide the parameter selection and improve interpretability. Next, we solve the inverse problem—recovering unknown model parameters from observed outputs—using gradient-based optimization with automatic differentiation. By reparametrizing inputs through bounded transformations, we ensure physiological plausibility throughout the estimation process. This approach reliably identifies key parameters such as vascular resistances, chamber properties, and shunt characteristics, with typical convergence times under two minutes.

To quantify uncertainty in the inverse solution, we propagate input data noise through the inverse problem via a Monte Carlo approach. For each sampled clinical measurement set, we solve the parameter estimation problem using the surrogate, then propagate the resulting parameter distribution through the model with the shunt in place. This yields output distributions (e.g., for pressures, stroke volumes, flow ratios) that inform confidence in predicted outcomes.

Compared to PCE and GP, neural networks emerge as the most robust choice. They support fast training on large datasets, integrate naturally with automatic differentiation, and scale efficiently to high-dimensional input spaces. This makes them ideal candidates for real-time or near-real-time clinical inference tasks.

In conclusion, we propose a surrogate-enabled framework tailored to inverse problems in cardiovascular modeling, enabling rapid and personalized parameter estimation and UQ. This approach paves the way toward computationally efficient digital twins for clinical use.

Numerical cardiovascular modeling is a growing tool for clinical applications aimed at personalized medicine. As such, lumped parameter models offer computational efficiency, yet, require calibration with often sparse clinical data. This study [1] compares two established cardiac chamber models—Time-Varying Elastance (TVE) and Single-Fiber (SF) models —through sensitivity and identifiability analyses to assess their suitability for patient-specific applications. The case of a young pulmonary arterial hypertension (PAH) patient serves as the clinical context, although the methodology is applicable to other conditions.

The TVE and SF models were integrated into a lumped parameter closed-loop circulation capable of simulating whole-body hemodynamics. Patient-specific data from a 13-year-old with PAH were used to calibrate the models through inverse problem optimization employing the CMA-ES method. After successful tuning of the two models, sensitivity analysis was conducted in order to quantify the impact of input parameters on clinically relevant outputs, such as ventricular pressures and volumes, based on the total Sobol indices. Physiological constraints were enforced to ensure the outputs remained within clinically relevant bounds, while an extensive literature review had to be performed to define the input ranges. The identifiability of the sensitive parameter set can be then assessed using Profile Likelihood analysis (PLA). It is a step-wise process, which involves inverse problem solving (similarly to the calibration step) and evaluates whether a unique set of model parameters can be reliably estimated from the available clinical data.

The SF model demonstrated superior performance in reproducing patient-specific hemodynamic data, accurately capturing nonlinear ventricular pressure-volume dynamics and key parameters such as stroke volume and pressure levels. Sensitivity analysis identified dominant parameters affecting outputs, which showed that there is a significant interaction between parameters describing the systemic circulation and pulmonary hemodynamics, and vice versa. This highlights the importance of studying the whole circulation, particularly in diseases traditionally assumed to affect only one side. Identifiability analysis revealed that the SF model’s parameters were more reliably estimable than those of the TVE model, which showed limitations in the identification of key parameters such as ventricular and atrial elastances.

Despite the fact that the TVE model offers simplicity and computational efficiency (due to its linear nature), our comparative analysis in the setting of pulmonary hypertension indicates that the SF model is more suitable for personalized cardiac simulations. The limited physiological interpretability of the TVE model not only required more clinical data to find suitable personalized parameters but also made the determination of input ranges for the sensitivity analysis significantly more challenging. The SF model’s detailed representation facilitates better alignment with clinical data, which is essential for personalized medicine applications. Our study underscores the importance of cardiac modeling choice based on disease case study and data availability. This study also highlights the importance of comprehensive data collection, sensitivity analysis and model validation in advancing personalized medicine. As a future step, it would be insightful to compare non-linear extensions of the TVE model to the SF one.
[1] Haghebaert et al., J of Physiology, accepted

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.