This talk introduces a digital twin (DT) formulation for the optimal treatment of occluded carotid arteries. An occluded or stenotic carotid artery is a severe condition where plaque buildup (atherosclerosis) narrows or blocks the main arteries supplying blood to the brain, significantly increasing stroke risk. The main quantity of interest is the wall shear stress (WSS) i.e., the tangential component of the normal stress exerted by the blood on the arterial wall. Clinical evidence suggests that low and oscillating values of WSS are associated with the development of adverse events. However, the practical use of the WSS as a predictor is limited by the fact that it cannot be directly measured in a patient. We assume the availability of information from sparse 4D-MRI data and leverage graph neural networks to estimate the WSS, its time-averaged distribution, and the corresponding occlusion magnitude. These quantities are embedded within probabilistic graphical models (PGMs) to represent and propagate uncertainties in the system, enabling more accurate predictions and better decision-making [1-4]. Treatment considerations include pharmacological therapy, such as cardiac aspirin intake, and potential surgical intervention. The resulting DT provides a probabilistic, patient-specific characterization of WSS and occlusion severity, enabling uncertainty-aware decision support for treatment planning. REFERENCES [1] M. G. Kapteyn, J. V. R. Pretorius, and K. E. Willcox, “A probabilistic graphical model foundation for enabling predictive digital twins at scale”, Nature Computational Science, vol. 1, no. 5, pp. 337–347, 2021. [2] M. Torzoni, M.Tezzele, S. Mariani, A. Manzoni, and K. E. Willcox, “A digital twin framework for civil engineering structures”, Computer Methods in Applied Mechanics and Engineering, Vol. 418, p. 116584, 2024. [3] E. Varetti, M. Torzoni, M. Tezzele, and A. Manzoni, “Adaptive digital twins for predictive decision-making: Online Bayesian learning of transition dynamics”, arXiv:2512.13919, 2025. [4] Sel, K., Hawkins-Daarud, A., Chaudhuri, A. et al., “Survey and perspective on verification, validation, and uncertainty quantification of digital twins for precision medicine”, npj Digital Medicine, vol. 8, 40, 2025.