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Uncertainty Quantification in Cardiac Model Personalisation from Ultrafast Ultrasound
Camilla Ferrario, Maelys Venet, Olivier Villemain, Maxime Sermesant
TL;DR
Sparse measurements and interacting cardiac parameters make myocardial-mechanics personalisation uncertain, while SWE provides a stiffness-dynamics target that does not uniquely determine active parameters. The paper uses context-conditioned SBI with a subject-adapted 0D model to estimate parameter posteriors; among four prior-supported volunteers, posterior predictive RMSE fell by 89.7 ± 4.2% relative to the prior predictive median.
Problem
SWE-derived stiffness dynamics provide a more direct myocardial measure than pump-function metrics, but do not uniquely identify active mechanical parameters or which are constrained.
Source: §1 · p. 2Method
A subject-adapted 0D cardiovascular model and neural posterior estimation infer distributions over active parameters from SWE curve features and subject-specific context.
Source: §1 · p. 2, §2.2 · p. 3Results
RMSE fell from 12.61 ± 5.55 kPa for the prior predictive median to 1.14 ± 0.38 kPa for the posterior predictive median, an 89.7 ± 4.2% reduction; four of six subjects passed prior-support checks.
Source: §3 · p. 7Takeaways & Limitations
Posterior analysis found k0–kATP compensation, parameter-specific uncertainty, and weaker constraint of kSR, underscoring the role of prior-support checks in assessing subject representation.
Source: §3 · p. 8, §4 · p. 9Inference is conditional on the selected prior, feature-noise model, fixed passive and circulatory components, and simplified 0D assumptions that omit spatial heterogeneity and fibre architecture.
Source: §2.2 · p. 3, §3 · p. 8
Abstract
from arXiv · showhide
Cardiac model personalisation requires inferring mechanical parameters that are not directly measurable in vivo. Ultrafast ultrasound shear wave elastography (SWE) enables non-invasive tracking of myocardial stiffness dynamics over the cardiac cycle, providing a target for personalisation. However, mapping these observations to subject specific model parameters remains ill-posed, as multiple parameter sets can reproduce the same stiffness dynamics. We formulate SWE-informed personalisation as a statistical inference problem using simulation-based inference (SBI). Using a subject-adapted 0D cardiovascular model and neural posterior estimation, we estimate model-conditional posterior distributions over active stiffness scale k0, contraction rate kATP, and relaxation rate kSR, conditioned on SWE-derived curve features and subject specific context. Among six healthy volunteers, four passed objective prior-support diagnostics and were retained for quantitative posterior analysis. Curve-level RMSE against the observed SWE target decreased from 12.61 $\pm$ 5.55 kPa for the prior predictive median to 1.14 $\pm$ 0.38 kPa for the posterior predictive median, an 89.7 $\pm$ 4.2% reduction. Posterior analysis revealed parameter-specific uncertainty, k0-kATP compensation, weaker constraint of kSR, and the importance of prior-predictive diagnostics for assessing whether each subject is represented within the modelled SWE feature space. These results support SBI for uncertainty aware SWE-based personalisation, while identifying prior support and forward-model adequacy as key diagnostics.
1 Introduction
Sparse clinical measurements and interacting cardiac parameters make personalisation ill-posed, while SWE offers a more direct measure of myocardial stiffness dynamics. The paper introduces context-conditioned SBI to estimate distributions of active myocardial mechanics from SWE features and subject-specific context.
1 Introduction
- Cardiac model personalisation links measured signals to subject-specific mechanical properties and calibrates parameters from limited measurements such as motion, deformation, volumes, or pressure points.These observations are often sparse, and parameter interactions can allow similar observations to be explained by different parameter combinations.Source: §1 · pp. 1–2
- Sparse measurements and interacting parameters can leave cardiac personalisation ill-posed, with uncertain, correlated, or partially identifiable estimates.Reliable personalisation therefore requires quantifying which properties the measurements constrain, rather than reporting only a best-fit parameter vector [5,20,15].Source: §1 · p. 2
- SWE tracks myocardial stiffness more directly than global pump-function measures, but stiffness dynamics combine passive response, active force, and measurement variability.Consequently, fitting the stiffness curve alone cannot identify a unique set of active mechanical parameters or determine which are constrained.Source: §1 · p. 2
- SBI learns an approximate posterior from simulated data, addressing complex models with intractable likelihoods while neural methods can capture non-Gaussian uncertainty and parameter dependencies.The paper positions this application against prior cardiovascular SBI work focused primarily on haemodynamic biomarker estimation.Source: §1 · p. 2
- The paper introduces context-conditioned SBI with a subject-adapted 0D model and neural posterior estimation for inferring active-mechanics distributions from SWE features and subject context.Its preliminary healthy-volunteer evaluation uses posterior predictive checks and comparison with an optimisation-based point estimate.Source: §1 · p. 2
2 Methods
The methods use cycle-normalized SWE stiffness curves as observations and a context-adapted 0D cardiovascular model to simulate subject-specific stiffness. Feature-context samples from a shared prior are pooled to train neural posterior estimation, then evaluated with prior-support checks, posterior predictive summaries, and an optimisation-based reference.
2.1 Ultrafast SWE-derived stiffness target
- SWE acquisitions sampled 20 ECG-gated phases across the cardiac cycle, and spatially averaged shear-wave speed was converted to apparent Young’s modulus to form each subject’s normalized stiffness curve.The resulting curve was used directly as the observation for inference; acquisition and reconstruction followed established protocols.Source: §2.1 · p. 3
2.2 Context-adapted 0D cardiac model
- The reduced-order 0D simulator couples a thick-walled spherical left ventricle to closed-loop systemic RCR and pulmonary RC Windkessel circulation under an isotropic fibre assumption [4,8].Subject context includes ventricular volumes, septal thickness, heart rate, age, sex, and body surface area; HR, IVSd, and LVEDV set cardiac period and reference geometry.Source: §2.2 · p. 3
- Personalisation estimates a posterior over active stiffness amplitude k0, contraction rate kATP, and relaxation rate kSR, while passive, circulatory, and valve parameters remain fixed across subjects.The observation-level passive stiffness scale is calibrated per subject before SBI, and the simulated target combines active response with a precomputed passive component held fixed during inference.Source: §2.2 · p. 3
2.3 Context-conditioned SBI
- A hybrid 46-feature summary combines 16 scalar descriptors with 30 resampled trajectory values; scalar-only preliminary ablations degraded posterior predictive performance.Feature-noise augmentation, pooled standardization, and concatenation with subject context produce samples pooled across cases for amortized neural posterior estimation and subject-specific posteriors.Source: §2.3 · pp. 4–5, Figure 1 · p. 4
2.4 Experimental setup
- The frozen pooled setup used an independent bounded log-Gaussian prior over k0, kATP, and kSR, with 1,000 successful prior simulations per subject and 20 feature-noise augmentations per simulation.Across six evaluated subjects, this yielded 120,000 pooled training samples for the shared NPE model.Source: §2.4 · p. 6
2.5 Evaluation
- Cases were retained for quantitative analysis only if standardized observed features stayed within 3 and at least 1,000 posterior draws fell within prior bounds among 5×10^5 candidates.Posterior predictive checks assessed target reproduction under the simulator and observation model, while parameter summaries included credible intervals and pairwise dependencies.Source: §2.5 · p. 6
- CMA-ES supplied a diagnostic point reference using the same subject context, passive baseline, and active-parameter bounds as SBI, with the best loss selected across 10 seeded runs.Its objective combined normalized MAE, correlation mismatch, and peak mismatch; the selected fit was not treated as ground truth.Source: §2.5 · pp. 6–7
3 Results and Discussion
Among four prior-supported cases, posterior predictive fitting substantially improved agreement with SWE, while parameter identifiability remained uneven and conditional on the model assumptions.
Prior-support diagnostics
- Four of six subjects passed both prior-support criteria; the other two were retained as support/model-adequacy cases, not forward-simulation failures.One case yielded only one valid in-prior sample from 5 × 10^5 candidate draws; another had systolic up-slope z = 3.14 and no valid in-prior sample.Source: §3 · p. 7
Posterior predictive performance
- RMSE fell from 12.61 ± 5.55 to 1.14 ± 0.38 kPa (89.7 ± 4.2% reduction) versus the prior predictive median, with R2 of 0.996 ± 0.001.Table 1 reports RMSE in kPa against the observed SWE target, with reduction relative to the prior predictive median.Source: §3 · p. 7, Table 1 · p. 7
- Cases A–C had accurate medians and near-complete 90% PI coverage, whereas Case D had the largest post-peak RMSE and lower coverage.The residual mismatch in Case D was consistent with a timing or relaxation mismatch.Source: §3 · p. 7
Posterior uncertainty and identifiability
- k0 was generally well constrained; kATP showed limited practical identifiability and negative k0–kATP correlation (r = −0.84 ± 0.15), while kSR information was weaker.Wider-prior experiments shifted kATP distributions; synthetic-recovery coverage was 26.5% for kSR.Source: §3 · p. 8, Figure 3 · p. 9
Limitations
- Identifiability is conditional on the prior, observation model, fixed passive component, and 0D model, which omits spatial heterogeneity, fibre architecture, and subject-specific loading.Observed parameter dependencies may reflect both limited SWE information and structural model mismatch.Source: §3 · p. 8
Diagnostic comparison with CMA-ES
- SBI posterior predictive medians had lower RMSE than CMA-ES estimates in all four cases, but the comparison is diagnostic, not competitive, because one summarizes a distribution and the other a point fit.Differences should not be read as evidence of unique parameter recovery.Source: §3 · p. 8
4 Conclusion
The study presents context-conditioned SBI for personalising active myocardial mechanics from SWE and finds improved posterior predictive agreement in four of six healthy volunteers. Its conclusions remain preliminary, conditional on modelling choices and limited by the small healthy-volunteer sample.
Conclusion
- Among six healthy volunteers, four met prior-support criteria and showed improved posterior-predictive agreement, while two were inadequately represented by the prior-predictive distribution.The study presents context-conditioned SBI for probabilistic personalisation of active myocardial mechanics from SWE-derived stiffness dynamics.Source: §4 · p. 9
- Posterior analysis identified k0–kATP compensation, parameter-specific uncertainty, and weaker constraint of kSR, but predictive agreement does not establish unique parameter recovery.Reported uncertainty is conditional on the selected prior, feature-noise covariance, precomputed passive component, fixed circulatory parameters, and simplified 0D model.Source: §4 · p. 9
- The small healthy-volunteer sample limits assessment of between-subject variability and generalisability to pathological populations; clinical translation requires larger pathological cohorts and improved modelling and uncertainty calibration.The conclusion also calls for validation and subject-specific modelling of passive mechanics and loading.Source: §4 · p. 9