Electrical lumped model for arterial vessel beds

Abstract

Numerous electrical analog models of the circulatory system have been proposed. However, conventional models are either too simple, focusing exclusively on heart function, or overly complex, characterizing arteries in excessive detail. The vessel beds, which comprise arteries, capillaries and veins, are well known to be responsible for most of the pressure drop in blood pressure and to dominate the draining of blood flow. Consequently, electrical analog models of the circulatory system should pay more attention to the vessel beds. This investigation divided the arterial system into several aortic segments with vessel beds, and proposed a model that used electrical lumped elements to represent the vessel beds. The model was adopted to simulate blood pressure propagation by considering each vessel bed as an isolated subsystem. The transfer function between the terminals of isolated subsystems was used to identify the electrical components of the lumped elements that characterized the vessel beds. Simulation results reveal that the compliance and impedance of the vessel beds are larger than in previous models that focused on the aorta or arteries. The proposed electrical lumped model could deal with much more information than the simple models due to the lumped element structure. Furthermore, its isolated subsystem approach also makes the proposed model significantly easier to use than the complex models.

Introduction

Numerous models have been developed to investigate circulatory system behavior, including neuroregulation, gas exchange, and arterial pulse propagation [1], [2]. Models for investigating arterial pulse propagation have attracted special attention because of their physiological and clinical applications [3], [4], [5]. Models of arterial pulse propagation typically employ one of two approaches, namely electrical analog [6], [7], [8] and finite-element techniques [9]. Meanwhile, the electrical analog technique is further divided into electrical lumped [6], [7], [8] and transmission line models [10], [11]. Recently, some new models [12], [13] and methods [14], [15] have also been proposed. However, the electrical lumped models have proved very useful for investigating arterial blood pressure and blood flow.

Blood pressure and blood flow react to conditions of the arterial system. The Navier–Stokes equations accurately depict the relation between blood pressure and blood flow, which is characterized by vessel resistance, vessel compliance and blood inertia. Under some assumptions, the Navier–Stokes equations resemble the voltage–current relations of an electrical circuit. Consequently, numerous electrical lumped models have been designed to simulate the arterial system. Most electrical lumped models comprise a number of basic elements including resistors, capacitors, and inductors [16]. The simplest model simply contains a pumping heart and a single lumped element for all peripheral vessels [17], [18], and generally focuses on heart function. On the other hand, some complex models may contain hundreds of elements for each aortic segment of the major arteries [9], [19], and simulate artery characteristics in detail. Both the simple and the complex models give little consideration to vessel beds containing various vessels, including arteries, capillaries and veins. In fact, the vessel beds are responsible for most of the pressure drop in blood pressure and to dominate the draining of blood flow. Consequently, electrical lumped models of the arterial system should pay more attention to the vessel beds. Thus, this study presents an electrical lumped model similar to Noordergraaf's electrical analogous model but focuses on the vessel beds. The proposed model determines its electrical components using the blood pressure propagated along the aorta and the relative transfer functions. The relative values of the electrical components can be estimated from blood pressure alone. Combined with measurements of cardiac output, the novel electrical lumped model has the potential to characterize the vessel beds for clinical applications.