TDSpy: An open-source implementation of time delay stability analysis

Time Delay Stability (TDS) is an established tool for analyzing the interaction between physiological systems in the human organism. Time series are measured with sensors from different organ systems and are analyzed pairwise. Each pair is characterized by a TDS link strength and by combining these to a network, insights into underlying physiological mechanisms can be obtained. Computing TDS is based on heuristic computations with multiple open parameters. In the past, research groups working with TDS have implemented their own algorithms in different programming languages, which posed the risk of differences between implementations and parameters, leading to a lack of reproducibility. Therefore, we propose a reference implementation written in Python 3, entitled TDSpython ( TDSpy ) that we make publicly available via the Python Package Index (PyPI). In this paper, we give a comprehensive description of the implementation, demonstrate its usage on publicly-available sleep research data, and evaluate its suitability by reproducing published studies. In addition, we apply TDSpy to data from comatose patients, emphasizing its generalizability.