Recent studies suggest that the interaction between the brain and heart plays a key role in cognitive processes, and measuring these interactions is crucial for understanding the interaction between the central and autonomic nervous systems. However, studying this bidirectional interplay presents methodological challenges, and there is still much room for exploration. This paper presents a new computational method called the Poincaré Sympathetic-Vagal Synthetic Data Generation Model (PSV-SDG) for estimating brain-heart interactions. The PSV-SDG combines EEG and cardiac sympathetic-vagal dynamics to provide time-varying and bidirectional estimators of mutual interplay. The method is grounded in the Poincaré plot, a heart rate variability method to estimate sympathetic-vagal activity that can account for potential non-linearities. This algorithm offers a new approach and computational tool for functional assessment of the interplay between EEG and cardiac sympathetic-vagal activity. The method is implemented in MATLAB under an open-source license. • A new brain-heart interaction modeling approach is proposed. • The modeling is based on coupled synthetic data generators of EEG and heart rate series. • Sympathetic and vagal activities are gathered from Poincaré plot geometry. Specifications table Subject area: Neuroscience More specific subject area: Autonomic Neuroscience Name of your method: Poincaré Sympathetic-Vagal Synthetic Data Generation (PSV-SDG) Name and reference of original method: First proposal to study heart rate variability with Poincaré plots, by Woo et al. [1] Modeling of heart rate oscillations using Poincaré plots, by Brennan et al. [2] Modeling of EEG signals using adaptive Markov process, by Al-Nashash et al. [3] Original proposal of brain-heart modeling through synthetic data generation models, by Catrambone et al. [4] Alternative proposal of brain-heart modeling through synthetic data generation models, by Candia-Rivera et al. [5] Resource availability: https://github.com/diegocandiar/brain _ heart _ psv _ sdg