Real-Time Surrogate Modeling for Personalized Blood Flow Prediction and Hemodynamic Analysis

Sokratis J. Anagnostopoulos; George Rovas; Vasiliki Bikia; Theodore G. Papaioannou; Athanase D. Protogerou; Nikolaos Stergiopulos

cs.LGApr 3, 2026

Real-Time Surrogate Modeling for Personalized Blood Flow Prediction and Hemodynamic Analysis

Authors: Sokratis J. Anagnostopoulos, George Rovas, Vasiliki Bikia, Theodore G. Papaioannou, Athanase D. Protogerou, Nikolaos Stergiopulos

Organizations: Laboratory of Hemodynamics and Cardiovascular Technology, EPFL, Lausanne, Switzerland · Stanford DBDS and HAI, Stanford University, Palo Alto, USA · Medical School, National and Kapodistrian University of Athens, Athens, Greece

Abstract

Cardiovascular modeling has rapidly advanced over the past few decades due to the rising needs for health tracking and early detection of cardiovascular diseases. While 1-D arterial models offer an attractive compromise between computational efficiency and solution fidelity, their application on large populations or for generating large in silico cohorts remains challenging. Certain hemodynamic parameters like the terminal resistance/compliance, are difficult to clinically estimate and often yield non-physiological hemodynamics when sampled naively, resulting in large portions of simulated datasets to be discarded. In this work, we present a systematic framework for training machine learning (ML) models, capable of instantaneous hemodynamic prediction and parameter estimation. We initially start with generating a parametric virtual cohort of patients which is based on the multivariate correlations observed in the large Asklepios clinical dataset, ensuring that physiological parameter distributions are respected. We then train a deep neural surrogate model, able to predict patient-specific arterial pressure and cardiac output (CO), enabling rapid a~priori screening of input parameters. This allows for immediate rejection of non-physiological combinations and drastically reduces the cost of targeted synthetic dataset generation (e.g. hypertensive groups). The model also provides a principled means of sampling the terminal resistance to minimize the uncertainties of unmeasurable parameters. Moreover, by assessing the model's predictive performance we determine the theoretical information which suffices for solving the inverse problem of estimating the CO. Finally, we apply the surrogate on a clinical dataset for the estimation of central aortic hemodynamics i.e. the CO and aortic systolic blood pressure (cSBP).

Figures & tables

Parameter	Range	Mean	SD
Age (years)	35 - 57	45.76	5.61
PWV (m/s)	4.5 - 9.0	6.4	0.92
Height (cm)	152 - 190	169.12	7.92
Weight (kg)	48 - 105	72.89	12.13
SBP (mmHg)	102 - 169	129.64	14.08
HR (bpm)	43 - 85	63.1	8.07

Table 1: In silico dataset parameter range and distribution.

Figure 1: Real-time prediction workflow : The Asklepios dataset is used to draw physiologically correlated values within the parameter space which can be clinically estimated noninvasively. The dataset is augmented using LHS method and 2000 1-D forward simulations are performed using the 1-D cardiovascular code. The parameter space can be adjusted depending on the physiological range depending on the study. The surrogate model is trained either in forward or inverse mode to provide real-time hemodynamic predictions.

Figure 2: Training performance: Indicative convergence of the forward surrogate mode. (a) Mean-squared error loss over 2000 epochs for training and test sets. The convergence minimum indicates no overfitting and good model generalization. (b) Correlation and Bland-Altman plots: agreement between predicted and measured blood pressures for the brachial DBP (left) and SBP (right) network outputs.

Figure 3: Pair-wise parameter sensitivity: The sensitivity heatmap of varying pair-wise parameters (while the rest are held fixed), reveals the parameters with the highest influence on the diastolic/systolic blood pressure are the terminal resistance $R_{T}$ , the $CO$ , the compliance $C$ and the $HR$ . For the pulse pressure $(PP)$ , the most dominant parameters are the $CO$ , the $R_{T}$ and $R_{C}$ . The geometry, as well as the terminal compliance have negligible influence in the $\Delta P$ over the full parameter range variation.

Figure 4: Pair-wise contour maps: The hemodynamic interactions between each parameter pair (while the rest are held fixed) cause distinct 2-D variations in the resulting pressure fields for both $SBP$ (top), and $DBP$ (bottom). The white points represent the in silico patients used for the training.

Figure 5: Pressure iso-surfaces: Plotting the most sensitive hemodynamic parameters reveal distinct regions of low, normal and hypertensive patients for the $DBP$ (left) and $SBP$ (right). The regions outside this range are non-physiological cases.

Figure 6: Population matching: (a) The distribution of naively sampled terminal resistance ( $R_{T}$ ) widens the output pressure distributions, even though the rest of the known parameters are sampled directly from the clinical dataset of Asklepios. (b) Constraining only the range of pressures indicates that the 1-D model is able to closely match the clinical distributions of Asklepios for both $DBP$ and $SBP$ , while the distribution of $R_{T}$ takes a triangular shape.

Figure 7: $CO$ identification: (a) Using only the noninvasively obtainable parameters ( $L$ , $D$ , $C$ , $HR$ , $SBP$ , $DBP$ ) yields high correlation but large limits of agreement, reflecting a strong indication of non-uniqueness for the inverse mapping. (b) Introducing an extra pressure reading at the radial artery (b) or the terminal resistance and compliance ( $R_{T}$ , $C_{T}$ ) (c), resolves the ambiguity and recovers $CO$ with near-perfect accuracy.

Case	$r$	$R^{2}$	Error (%)	$\Delta\overline{\sigma}_{\mathrm{u}}^{2}$ (%)
$f_{\theta}(X)$	0.942	0.887	0.6	11
$f_{\theta}(X,rDBP,rSBP)$	0.984	0.968	0.32	2.7
$f_{\theta}(X,rDBP)$	0.945	0.893	0.58	9.6
$f_{\theta}(X,rSBP)$	0.982	0.964	0.3	3.1
$f_{\theta}(X,\lambda_{R_{T}},\lambda_{C_{T}})$	0.998	0.996	0.1	-
$f_{\theta}(X,\lambda_{R_{T}})$	0.998	0.996	0.12	0

Table 2: Inverse cases with the percentage of irreducible uncertainty

\Delta\overline{\sigma}_{\mathrm{u}}^{2}

Figure 8: $R$ - $C$ vs $CO$ grids: (a) Indicative patient contour show that the terminal resistance has a strong monotonic influence on $CO$ . (b) To isolate the effect of $C_{T}$ , we normalize each $R_{T}$ column with its max $CO$ value to reveal that there are at most 4 solutions of the same $C_{T}$ , which constrains the possible combinations even when only $C_{T}$ is given as input along with $X$ .

Figure 9: Cardiac hemodynamics prediction: Using only noninvasive inputs $X$ , the surrogate (a) captures the dominant flow across the clinical dataset, while (b) it provides a very accurate estimate for the aortic pressure.

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