Non-integer Approach to Modelling Compartments of Cardiovascular Circulatory System

For predicting cardiovascular diseases, mathematical modelling of the cardiovascular system has been proven to be a powerful asset. The governing idea is to analyse it through compartments as multiple connected subsystems with inputs and outputs. In this paper, models were identified for four subsystems of input-output sequence (left ventricle - left atrium - ascending aorta - descending aorta - left common carotid artery) by modelling frequency response. The data set used for model identification consisted of blood pressure during four consecutive heart contractions of four circulatory segments from clinical trials performed on a pig. The goal is to discover a linear model with a non-integer order that succinctly represents the process, outperforming high-order autoregressive exogenous input (ARX) integer models. This model identification occurs non-parametrically, aiming to achieve the best smooth fit in the frequency domain by minimizing the difference between real measurements and model predictions using the particle swarm optimization (PSO) algorithm.