Simulation-based Inference for Cardiovascular Models

TL;DR

This work reframes the inverse problem of inferring cardiovascular biomarkers from biosignals as simulation-based inference (SBI), yielding posterior distributions that capture multi-dimensional, individualized uncertainty. By applying neural posterior estimation to a full-body 1D cardiovascular simulator, the authors demonstrate population- and per-individual uncertainty analyses across measurement modalities and noise levels, uncovering multi-modal posteriors and sub-populations. In-silico results show differential information content across modalities (e.g., digital PPG vs. radial APW) and robust calibration of the posterior, while in-vivo transfer to MIMIC-III data reveals HR can be transferred reasonably well but LVET transfer is hindered by misspecification, motivating model refinement. The paper argues that SBI provides richer, more actionable insights for cardiovascular modeling and precision medicine than traditional sensitivity analyses, and it outlines future directions for joint-modality simulators and data integration to improve real-world applicability.

Abstract

Over the past decades, hemodynamics simulators have steadily evolved and have become tools of choice for studying cardiovascular systems in-silico. While such tools are routinely used to simulate whole-body hemodynamics from physiological parameters, solving the corresponding inverse problem of mapping waveforms back to plausible physiological parameters remains both promising and challenging. Motivated by advances in simulation-based inference (SBI), we cast this inverse problem as statistical inference. In contrast to alternative approaches, SBI provides \textit{posterior distributions} for the parameters of interest, providing a \textit{multi-dimensional} representation of uncertainty for \textit{individual} measurements. We showcase this ability by performing an in-silico uncertainty analysis of five biomarkers of clinical interest comparing several measurement modalities. Beyond the corroboration of known facts, such as the feasibility of estimating heart rate, our study highlights the potential of estimating new biomarkers from standard-of-care measurements. SBI reveals practically relevant findings that cannot be captured by standard sensitivity analyses, such as the existence of sub-populations for which parameter estimation exhibits distinct uncertainty regimes. Finally, we study the gap between in-vivo and in-silico with the MIMIC-III waveform database and critically discuss how cardiovascular simulations can inform real-world data analysis.

Figures (10)

• Figure 1: A sketch of SBI for the analysis of 1D cardiovascular models and the corresponding uncertainty analysis performed at an individual level. Our results indicate that the estimation of left-ventricular ejection time (LVET) and systemic vascular resistance (SVR) from the digital PPG are dependent. There exists a sub-population of measurements for which both quantities are identifiable while there remains a bi-modal uncertainty for the respective other measurements.a: Simulator of the hemodynamics in the $116$ largest human arteries. b: The measurements generated from simulations following a meaningful prior distribution over the model's parameters. c: The neural posterior estimation algorithm learns a surrogate of the posterior distribution of the parameters of interest given the digital PPG. d: Two posterior distributions respectively corresponding to an individual measurement from each identified sub-population, highlighting the benefit of uncertainty representation at the individual level. e: The sub-sets of measurements corresponding to the two identified sub-population, revealing distinct morphological characteristics in each sub-group.
• Figure 2: Average size of credible intervals over the test population for credibility levels $68\%$ and $95\%$ of the learned posterior distributions. The x-axis denotes the signal-to-noise-ratio (SNR) for different types of measurements. Results are averaged over five training instances, the vertical bars report one standard deviation. The results are directly expressed in the physical units, in squared brackets, of the parameter considered. On simulated data, as the SNR increases, the posterior deviates from the prior distribution and the uncertainty over the parameters decreases. The information gain depends on the parameter and measurement considered, no measurement is uniquely better than all others.
• Figure 3: Uncertainty obtained from NPE vs. the Laplace's approximation around point estimates, representative of the sensitivity analyses performed in the literature. The colors denote the different populations considered (cf. Figure \ref{['fig:two_populations']}), the black lines denote the true value of the parameter, and the white star is the point estimate. The left top plot shows that NPE is almost perfectly calibrated whereas the Laplace's approximation is either over-confident or under-confident. The right top plot shows that NPE gives tighter credible intervals compared to Laplace's approximation which yields constant shape. The bottom plot compares the uncertainty representations for two different measurements respectively identified as uni-modal and bi-modal. Overall this figure shows that NPE (in red and blue) provides a more useful and accurate representation of uncertainty than Laplace's approximation (in gray).
• Figure 4: Mean absolute error (MAE) and correlation between the labels and point estimates extracted from the posterior distributions trained for different SNR values. The LVET's performance is compared to the predictions of a prior distribution conditioned on age and HR. The features predicting HR generalizes better than the one for LVET. The HR MAE decreases with decreasing SNR, indicating the posterior gains robustness to misspecification with decreasing SNR. The features extracted for LVET do not generalize to real-world data but seems to inform more than only age and HR as the posterior's correlation is higher than the prior one.
• Figure 5: Generation of a digital PPG observation in-silico. From left to right: a PPG signal is extracted from the 1D hemodynamics simulator, the same wave is concatenated to reach a length of 10 seconds, the 10-second segment is cropped randomly by two seconds, additive Gaussian noise is added (SNR $\approx 11$dB).