DuoPIC: Uncertainty-Aware Voxel-Level Digital Twins of Cerebral Perfusion with Transport PDEs in Acute Stroke

Anh Duong Tran; Quang-Anh N. D.; Toan Sy Pham; Trang H. Hoang; Minh N. Do; Duy Ton Mai; Huan X. Nguyen

cs.CVOct 20, 2026

DuoPIC: Uncertainty-Aware Voxel-Level Digital Twins of Cerebral Perfusion with Transport PDEs in Acute Stroke

Authors: Anh Duong Tran, Quang-Anh N. D., Toan Sy Pham, Trang H. Hoang, Minh N. Do, Duy Ton Mai, Huan X. Nguyen

Organizations: Vietnam National University · London Digital Twin Research Centre, Middlesex University · University of Alberta · College of Engineering and Computer Science, VinUniversity ·

Abstract

Digital twins of cerebral perfusion relate tracer dynamics to cerebral blood flow (CBF), blood volume (CBV) and mean transit time (MTT), but must be data-driven, physically consistent and uncertainty-aware. We introduce DuoPIC, a digital twin that needs no reference maps, in which a Windkessel flow model drives a tracer transport partial differential equation (PDE). A population-level neural closure divides each region into fast and slow pathways with tracer mass and MTT conserved by construction, and a tempered posterior quantifies the uncertainty of every estimate. Its voxel maps set the state of the art for lesion detection on ISLES'17 MR (AUC 0.745) and ISLES'24 CT (0.743). On held-out patients, the neural PDE reduced the compartment's reconstruction error by 19% and lifted 95% MTT interval coverage from 88% to 94%. Code: https://github.com/detinatran/duopic

Figures & tables

Figure 1: Overview of DuoPIC. (a) Input data. (b) ROI preparation with reference-free priors and an automatic AIF. (c) Neural transport model, in which Windkessel flow and a delayed, dispersed input drive a fast and a slow tube split by a shared network that conserves tracer mass and MTT. (d) Voxel maps (ROI level $\times$ texture, or voxel fit) and their uncertainty.

Figure 2: Mean residual (measured $-$ fitted, relative to the peak) around the bolus peak, $\pm 2$ standard errors, for HemoPIC [ 9 ] and DuoPIC; GM, WM: lesion-free ROIs; lesion: ROIs over 20% infarcted; $n$ : number of ROIs.

Figure 3: Uncertainty maps for the compartment (top) and the neural PDE (bottom), with the final infarct in black. CBF is divided by its brain median and the others by the estimate.

Figure 4: CBF, CBV and MTT of one ISLES’17 patient relative to the brain median, with the final infarct in red, from the ISLES maps, HemoPIC [ 9 ] and DuoPIC, with the lesion AUC of each map (best in bold).

Metric	Compart.	PDE	Neural PDE
Brain nRMSE $\downarrow$	0.116	0.108	0.094
Lesion nRMSE $\downarrow$	0.271	0.277	0.265
CBF coverage (%) $\to$ 95	97.0	-	98.2
MTT coverage (%) $\to$ 95	88.1	-	93.8
$\tau$ coverage (%) $\to$ 95	70.3	-	78.4
CBF width (%) $\downarrow$	85	-	72

Table 1: Held-out diagnostics. Parameter coverage: semi-synthetic; width: median 95% interval / value; nMSE: hidden-frame error, ROI median; -: not evaluated.

Method	CBF	CBV	MTT	Mean	AP
ISLES maps	$0.745$	$0.584$	$0.700$	$0.676$	$0.085$
HemoPIC [ 9 ]	$0.773$	$0.592$	$0.722$	$0.696$	$0.104$
oSVD [ 17 ]	$0.782$	0.623	$0.759$	$0.721$	$0.109$
DuoPIC, compartment	$0.790$	$0.552$	$0.766$	$0.703$	$0.113$
DuoPIC, PDE	$0.787$	$0.555$	$0.774$	$0.705$	$0.113$
DuoPIC, neural PDE	$0.788$	$0.561$	$0.768$	$0.706$	$0.113$

Table 2: Lesion AUC, 36 ISLES’17 patients with an accepted AIF, Mean: map-averaged AUC; AP: average precision.

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Digital twins are virtual models synchronized with real systems to support monitoring, prediction, simulation, and decision-making.

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Physics-informed neural networks (PINNs) have shown promise in addressing the ill-posed deconvolution problem in computed tomography perfusion (CTP) imaging for acute ischemic stroke assessment. However, existing PINN-based approaches remain deterministic and do not quantify uncertainty associated with violations of physics constraints, limiting reliability assessment. We propose Evidential Perfusion Physics-Informed Neural Networks (EPPINN), a framework that integrates evidential deep learning with physics-informed modeling to enable uncertainty-aware perfusion parameter estimation. EPPINN models arterial input, tissue concentration, and perfusion parameters using coordinate-based networks, and places a Normal--Inverse--Gamma distribution over the physics residual to characterize voxel-wise aleatoric and epistemic uncertainty in physics consistency without requiring Bayesian sampling or ensemble inference. The framework further incorporates physiologically constrained parameterization and stabilization strategies to promote robust per-case optimization. We evaluate EPPINN on digital phantom data, the ISLES 2018 benchmark, and a clinical cohort. On the evaluated datasets, EPPINN achieves lower normalized mean absolute error than classical deconvolution and PINN baselines, particularly under sparse temporal sampling and low signal-to-noise conditions, while providing conservative uncertainty estimates with high empirical coverage. On clinical data, EPPINN attains the highest voxel-level and case-level infarct-core detection sensitivity. These results suggest that evidential physics-informed learning can improve both accuracy and reliability of CTP analysis for time-critical stroke assessment. Source code is available at https://github.com/jhlee0619/EPPINN.

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