Complex dynamics in a fractional order nephron pressure and flow regulation model

Abstract

Cardiovascular diseases can be attributed to irregular blood pressure, which may be caused by malfunctioning kidneys that regulate blood pressure. Research has identified complex oscillations in the mechanisms used by the kidney to regulate blood pressure. This study uses established physiological knowledge and earlier autoregulation models to derive a fractional order nephron autoregulation model. The dynamical behaviour of the model is analyzed using bifurcation plots, revealing periodic oscillations, chaotic regions, and multistability. A lattice array of the model is used to study collective behaviour and demonstrates the presence of chimeras in the network. A ring network of the fractional order model is also considered, and a diffusion coupling strength is adopted. A basin of synchronization is derived, considering coupling strength, fractional order or number of neighbours as parameters, and measuring the strength of incoherence. Overall, the study provides valuable insights into the complex dynamics of the nephron autoregulation model and its potential implications for cardiovascular diseases.