This paper presents a novel framework integrating Bayesian physiological modeling with optimal control strategies to achieve uncertainty-aware, personalized hemodynamic regulation during fluid resuscitation. An uncertainty-aware variational autoencoder state-space model (UVAE-SSM) was first developed to capture the dynamical relationship between mean arterial pressure (MAP) and fluid infusion using limited data, while explicitly modeling aleatoric uncertainty (i.e., randomness in the measurements, such as sensor noise). Then, a Bayesian nonlinear state-space model (BNSSM) was developed by utilizing Bayesian neural networks (BNNs) to capture epistemic uncertainty arising from physiological and patient-specific variability, enabling the creation of a virtual patient generator (VPG). Building on this uncertainty-aware modeling framework, a stochastic radial basis function model predictive control (sRBF-MPC) algorithm was designed to track the MAP target while satisfying physiological constraints. Finally, an online fine-tuning algorithm was developed to adapt the nominal UVAE-SSM using streaming VPG data, enabling progressive personalization during closed-loop therapy. Simulation results across unseen animal subjects and an independent human clinical dataset demonstrated the strong predictive accuracy and cross-population generalizability of the UVAE-SSM and BNSSM models. Closed-loop evaluations confirmed that the proposed sRBF-MPC framework achieved stable MAP regulation while providing better risk-aware control compared to quadratic MPC (Q-MPC) and stochastic quadratic MPC (sQ-MPC). Overall, the proposed framework accounts for inter- and intra-patient variability through online model adaptation, offering a promising step toward uncertainty-aware, personalized hemodynamic modeling and control in critical care.
Figures & tables
Fig. 1: Proposed uncertainty-aware modeling framework. (a) UVAE-SSM as nominal model: The encoder maps a sliding window of NA MAP measurements and infusion rates (yk−NA:k,uk−NA:k) to the parameters (μx,σx) of a Gaussian latent distribution. A latent state xk is drawn via the reparameterization trick and passed to the deterministic transition network, which predicts the next latent state x^k+1 given (xk,uk) . The probabilistic decoder maps the latent state to a predictive MAP distribution N(μy,σy2) , explicitly capturing aleatoric uncertainty in the hemodynamic output. Dashed lines indicate training-only connections used to provide supervision targets for the transition loss. (b) BNSSM as VPG : The encoder and decoder form a deterministic autoencoder that maps observations to latent states and reconstructs MAP. The transition function fβ(xk,uk) is implemented as a BNN, where weights β are treated as random variables with variational posterior qη(β) , approximated via Bayes by Backprop. At inference, β is sampled once per complete simulation trajectory from qη(β) ; each distinct draw yields one virtual patient realization.
Fig. 2: Structure of the closed-loop fluid resuscitation framework with online personalization.
Fig. 3: MAP prediction for held-out animal test subjects using the proposed UVAE-SSM and the lumped hemodynamic model [ 6 ] .
Fig. 4: MAP prediction for human subjects using UVAE-SSM.
UVAE-SSM (Animal)
Lumped Model (Animal)
UVAE-SSM (Human)
Metric
Subject1
Subject2
Subject1
Subject2
Subject1
Subject2
Subject3
Subject4
Subject5
Subject6
RMSE (%)
4.66
3.07
7.74
7.19
2.49
0.86
0.91
2.71
0.54
0.53
MAE (%)
2.10
1.88
5.84
5.38
1.76
0.59
0.44
1.14
0.38
0.38
MDAPE (%)
0.65
1.02
5.57
3.81
1.13
0.39
0.23
0.49
0.25
0.26
TABLE I: MAP prediction performance of the UVAE-SSM on held-out animal and human test subjects. The lumped hemodynamic model [ 6 ] is included as a physiologically grounded baseline for the animal subject evaluation.
Fig. 5: MAP prediction on held-out animal test subjects using the VPG. The dashed line shows the ensemble mean over N=50 virtual patients.
Fig. 6: MAP prediction on held-out human clinical test subjects using the VPG.
VPG (Animal)
VPG (Human)
Metric
Subject1
Subject2
Subject1
Subject2
Subject3
Subject4
Subject5
Subject6
RMSE (%)
6.91
3.35
2.38
0.87
0.54
0.63
0.42
0.57
MAE (%)
4.01
2.04
2.04
0.60
0.43
0.42
0.31
0.42
MDAPE (%)
1.84
1.13
1.71
0.32
0.40
0.20
0.21
0.33
TABLE II: MAP prediction performance of the VPG on held-out animal and human test subjects
Fig. 7: Closed-loop MAP regulation under four hemorrhage scenarios comparing Q-MPC, sQ-MPC, and sRBF-MPC. Each panel shows the patient MAP trajectory (top) and the corresponding infusion rate (bottom). The light-red bands mark the active hemorrhage window ( t=0 – 15 min); The light-yellow region marks the pre-control phase, during which no infusion is applied. The dotted vertical line at t=30 min marks controller activation. Dashed purple vertical lines at t=60,90,120, and 150 min indicate periodic fine-tuning events. The dashed gray and red horizontal lines indicate the MAP target (80 mmHg) and the safety floor (60 mmHg), respectively.
Scenario
Controller
RMSE (%)
MAE (%)
MDAPE (%)
Below 60 mmHg (%)
Total Infusion (mL)
Solve Time/iteration (ms)
1
Q-MPC
11.09
7.61
4.58
2.9
3100.8
27.5±17.3
sQ-MPC
10.67
7.69
4.52
2.8
3011.8
62.3±65.7
sRBF-MPC
8.13
5.67
2.57
0.6
3364.4
255.9±326.0
2
Q-MPC
3.67
3.44
3.40
0.0
2145.8
14.0±6.9
sQ-MPC
3.68
3.45
3.40
0.0
2143.5
28.8±15.2
sRBF-MPC
2.20
2.04
2.10
0.0
2663.8
55.4±31.3
TABLE III: Closed-Loop Performance Comparison of Q-MPC, sQ-MPC, and sRBF-MPC Across Four Hemorrhage Scenarios