At Gdańsk University of Technology, a team from the Faculty of Applied Physics and Mathematics develops mathematical methods for applications in medicine. Its members include, among others, Grzegorz Graff, Paweł Pilarczyk, Justyna Signerska-Rynkowska, Beata Jackowska-Zduniak, Katarzyna Tessmer and Agnieszka Bartłomiejczyk. This work forms part of the applied mathematics research at Gdańsk Tech, which joined ECMI in 2025.
Mathematics for Understanding Cardiovascular Signals
An important strand of this research is devoted to understanding cardiovascular regulation, with particular attention to the relationships between heart rate, blood pressure and breathing in health and disease.
To address these questions, the team works in cooperation with clinicians from the Medical University of Gdańsk and physicists from the University of Gdańsk within the Fahrenheit Union of Universities in Gdańsk (FarU). The collaboration combines nonlinear dynamics, measures of complexity and topological data analysis with the physiological expertise needed to interpret cardiovascular recordings.
Ordinal analysis with ties and tolerance provides a useful way to describe changes in heartbeat intervals across the breathing cycle. In a study reported in Biomedical Signal Processing and Control, this method was applied to daytime cardiorespiratory recordings. The analysis provided a quantitative characterisation of the interactions between respiration and heart rate.
A topological approach uses persistent homology to represent variations in heartbeat intervals through persistence diagrams. Topological descriptors extracted from these diagrams were used to build classification models in a study published in PLOS ONE. In the studied dataset, several models distinguished healthy participants from patients with ischaemic stroke more effectively than the tested models based on standard heart rate variability measures.
Interactions between heart rate and blood pressure can also be quantified using ordinal patterns and entropy measures. In a study published in Chaos, these measures were combined with machine learning to build a compact classifier. It distinguished participants with obstructive sleep apnoea from controls, outperforming comparable models based on conventional variability measures in the study.
This exchange has been supported by workshops held at Gdańsk Tech in recent years, including the meetings in November 2024 and November 2025. Topics have ranged from entropy and computational topology to causal inference and cardiorespiratory interactions.
A Visegrad Partnership and a Workshop in Martin
A new Visegrad project will support the next stage of this collaboration. Causality Methods for Cardiovascular Disease Diagnostics and Risk Stratification in V4 (Visegrad Grant No. 22620137) aims to develop mathematical and AI methods for studying causal interactions in physiological recordings, with the goal of supporting cardiovascular diagnosis and risk assessment. Coordinated by Grzegorz Graff, with Paweł Pilarczyk co-leading the Gdańsk Tech team, it brings together Gdańsk Tech, the Medical University of Gdańsk, Comenius University’s Jessenius Faculty of Medicine in Martin and the Wigner Research Centre for Physics.
The project’s opening workshop, Cardiovascular and Cardiorespiratory Interactions – From Physiological Mechanisms to Clinical Applications, will take place at the Jessenius Faculty of Medicine in Martin, Slovakia, on 2–4 November 2026. The meeting will bring mathematicians and biomedical researchers together to define shared research questions and develop further cooperation.
The project is funded through the International Visegrad Fund’s Visegrad Grant programme, with additional support from the Ministry of Foreign Affairs of the Republic of Korea.