Med.& Biol. Eng. &Comput., 1980, 18,709 718 Multi-branched model of the human arterial system A. P. Avolio Medical Professorial Unit, St. Vincent's Hospital, Darlinghurst2010, Sydney, N.S.W. Australia Abstract--A model of the human arterial system was constructed based on the anatomical branching structure of the arterial tree. Arteries were divided into segments represented by uniform thin-walled elastic tubes with realistic arterial dimensions and wall properties. The configuration contains 128 segments accounting for all the central vessels and major peripheral arteries supplying the extremities including vessels of the order of 20 mm diameter. Vascular impedance and pressure and flow waveforms were determined at various locations in the system and good agreement was found with experimental measurements. Use of the model is illustrated in investigating wave propagation in the arterial system and in simulation of arterial dynamics in such pathological conditions as arteriosclerosis and presence of a stenosis in the femoral artery. Keywords--Arterial branching, Arterial model Elastic tubes, Vascular impedance, Wave reflection Nomenclature p = blood density Co = pulse wave velocity cr = Poisson ratio for arterial wall 2 J z (o~j 3/2) FIB = the expression ~j3/2Jo(~j3/2). where Jo and Jl are Bessel functions of the first kind, and order zero and one, respectively, and ct = Rox~P/P 7 = propagation constant co = angular frequency E = Young's modulus of arterial wall h = wall thickness Ro = internal radius of arterial segment qw = viscoelasticity of the arterial wall F = reflection coefficient /~ = blood viscosity 1 Introduction SINCE William Harvey established the concept of circulation of blood in 1628, numerous attempts have been made at gaining insight into the physical rela- tionship between the forces involved in propelling blood in the complicated anatomical structure of the circulatory system. The fact that the arterial tree First received 12th July 1979 and in final form 22nd January 1980 0140-0118/80/060709 + 10 SO1 "50/0 9 IFMBE: 1980 transforms intermittent flow from the left ventricle to a more steady outflow was recognised by Hales in 1733. He described the arterial system as a single elastic chamber which later became known as the Windkessel model (FRANK, 1899). Although this simple concept is sometimes used in determination of cardiac output (McDONALD, 1974), it fails to explain the phenomenon of pulse wave propagation through- out the arterial tree as the inherent property of the simple Windkessel model assumes an infinite pulse wave velocity. For a detailed analysis of the dynamics of arterial blood flow, a model is required which includes the multi-branched configuration of the arterial system, and a description of the distributed nature of arterial properties. An accurate representa- tion is essential especially for the human arterial tree because of the numerous practical difficulties of obtaining a whole range of physical measurements in vivo. In developing the model described below, the systemic vasculature is divided into a multi-segment branching structure consisting of 128 arterial seg- ments arranged according to the anatomical architec- ture of the human arterial tree. This configuration includes all the central vessels and principal arteries supplying the extremities with each segment having realistic dimensions and arterial properties. Peri- pheral branches are terminated with a resistance giving a specified reflection coefficient. The number of segments included in the model is determined by the desired accuracy in calculating pressure and flow waveforms throughout the system with the added limitation imposed by the available computer storage capacity. Medical & Biological Engineering & Computing November 1980 709