Data-Driven Operational Bounds of Transmembrane Pressure for Modelling and Digital Twin Development in Haemodialysis and Haemodiafiltration.

Transmembrane pressure (TMP) is a central state variable in haemodialysis (HD) and haemodiafiltration (HDF), governing ultrafiltration dynamics, convective transport, and membrane performance. Although dialysis devices specify high maximum allowable pressure limits derived from in vitro testing and mechanical safety margins, the effective operating pressure space encountered under routine clinical conditions remains insufficiently quantified from a systems engineering perspective. In this study, aggregated real-world minimum-maximum TMP intervals collected from four geographically distributed dialysis centres were used to anchor a model-based characterisation of operational pressure ranges. To enable reproducible modelling and numerical exploration, Gaussian-based synthetic datasets were constructed from empirically observed pressure intervals while incorporating physiological and operational constraints. Across all centres, HD exhibited stable and narrowly distributed TMP values (typically 20-60 mmHg), whereas HDF operated within higher but well-defined pressure regimes (approximately 120-260 mmHg). Values above 300 mmHg were rare, and pressures exceeding 400 mmHg were not observed under routine conditions. Statistical tail modelling, extreme value theory, and unsupervised anomaly detection consistently identified such extreme pressures as structurally incompatible with the learned operational state space. These results provide quantitative engineering bounds for TMP that may be directly integrated into reduced-order models, control design, and digital twin development for dialysis systems. By constraining modelling environments to empirically supported pressure regimes, the proposed framework enhances numerical stability, prevents non-physical extrapolation, and supports physiologically realistic data-driven applications in biomedical engineering.