Arterial spin labeling (ASL) MRI quantifies in-vivo perfusion non-invasively. Hadamard-encoded sub-boluses improve  ASL efficiency , allowing estimation of Cerebral Blood Flow (CBF) and Arterial Transit Time (ATT) with minimal time penalty [1], following the Buxton model [2].

Physics-informed neural networks (PINNs) integrate differential equations into machine learning models, enhancing predictions with noisy or sparse data [3]. PINNs have been applied successfully in cardiovascular perfusion MRI  [4] and brain perfusion studies, enhancing robustness in perfusion CT [5] and infant ASL imaging [6].

This study implements a two-stage PINN for ASL perfusion quantification, using synthetic data from the Boston ASL Template and Simulator [7]. ATT, CBF, and M0 templates generate te-pCASL data via a Buxton-based simulator. The model, comprising two neural networks — one fitting the data and the other estimating model derivatives — quantifies CBF and ATT. Performance is evaluated using Structural Similarity Index Measure (SSIM), Pearson Correlation Coefficient (PCC) and percentage relative error.

Our framework accurately quantifies CBF (SSIM: 0.733, PCC: 0.940) and ATT (SSIM: 0.917, PCC: 0.993), performing similarly to nonlinear least squares (NLLS) (SSIM: 0.750, PCC: 0.940; SSIM: 0.406, PCC: 0.777).  Even under high noise conditions and without prior knowledge, it produces spatially smoother, more robust to noise maps than NLLS, which generates scattered outputs. Although PINN systematically overestimates ATT, it preserves clinically relevant patterns for both parameters. Further optimization is required for in vivo validation in healthy and pathological conditions.

This study validates the applicability of our two-stage PINN framework in a simulated scenario, demonstrating its effectiveness in estimating multiple parameters from noisy, sparse te-pCASL data.

Figure 1: Comparison of CBF estimation using PINN and NLLS methods. a) CBF maps predicted by PINN and NLLS, respectively b) Relative error (%) of each method compared to the simulated ground truth

Figure 2: Comparison of ATT estimation using PINN and NLLS methods. a) ATT maps predicted by PINN and NLLS, respectively. 2) Relative error (%) of each method compared to the simulated ground truth.

References:

[1] Woods et al., MagnReson Med. 2024; 92: 469–495.

[2] Buxton et al., Magn. Reson. Med. 1998; 40: 383-396.

[3] Karniadakis et al., Nat Rev Phys 2021; 3: 422–440.

[4] Raissi et al., Journal of Computational Physics 2019; 378: 686–707.

[5] de Vries et. al., Medical Image Analysis 2023; 90: 102971.

[6] Galazis et al., Front. Netw. Physiol. 2025; 5.

[7] Taso et al., J Neuroimaging. 2022; 32: 1080–1089.