Computational simulation of blood flow in human systemic circulation incorporating an external force field

Abstract

A quasi-one-dimensional non-linear mathematical model for the computation of the blood flow in the human systemic circulation is constructed. The morphology and physical modelling of the whole system (arteries, capillaries and veins) are completed by different methods for the different vessel generations. A hybrid method is used to solve the problem numerically, based on the governing equation (continuity, momentum and state equations), the input boundary conditions and the predetermined initial conditions. The two-step Lax-Wendroff finite-difference method is used to compute variables for each individual vessel, and the characteristic method is employed for the computation of internal boundary conditions of the vessel connection and the input and output system boundary conditions. Using this approach, blood flow, transmural pressure and blood velocity are computed at all vessel sites and for each time step. The pressure and flow waveforms obtained show reasonable agreement with clinical data and results reported in the literature. When an external conservative force field is applied to the system, the results computed from the model are intuitively correct. The term representing the external pressure added to the system by the muscle, which represents active control on the cardiovascular system, is also embodied in this model.

A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method

“…However, it is common [3,21,44,58] to ignore the inertial component which is relatively insignificant at low values of the Womersley parameter [42] = R √ / where is the angular frequency of a given harmonic. For example, the inertial component would be most significant in a large artery (say R = 3.5 cm) with a high-frequency oscillation.…”

“…To transmit information between co-located nodes, the characteristics will again be used. (Note: the following treatment is a generalization of that given in [5,44].) Consider a parent vessel p with N daughter vessels.…”

“…For example, Wippermann [74] modelled the valve in 1D, but this was not coupled to an arterial tree model. Regarding arterial tree models, the effects of the valve have been included implicitly by prescribing experimental aortic root pressures at the inlet [1,2,44,56]. While some [3,5] have ignored its effects completely by treating the heart as a perfect absorber during the whole cardiac cycle, others have idealized the valve so that during systole the heart is a complete absorber of backward waves while during diastole it is a complete reflector [9,15,16].…”

“…This technique is commonly used [1,29,36] along with 1D electrical analogs [15] but these do not account for non-linear effects, which are important particularly in the large arteries [5,21,43]. The non-linear equations have been discretized using the finite difference method [2,7,44], as well as various other methods such as the characteristic [16], Galerkin least-squares [6] and discontinuous Galerkin methods [3][4][5]. In this work, we use the recently developed locally conservative Galerkin (LCG) finite element method [45] to solve the governing equations.…”

Wave Propagation in a System of Coaxial Tubes Filled With Incompressible Media: A Model of Pulse Transmission in the Intracranial Arteries

“…The brain tissue is modelled as a standard viscoelastic solid based on the experimental results reported by Shuck & Advani (1972). The vessel radius and elastic properties are chosen to represent larger cranial and spinal arteries and are based on the values reported by Hilen et al (1986), Zagzoule & Marc-Vergnes (1986), and Sheng et al (1995). Based on the typical diameter of the anterior spinal artery of approximately 1 mm (Dommisse 1975) and the typical width of the vertebral canal of approximately 10-20 mm (Lang 1993), the minimal value of the parameter y 0 for the spine is approximately 10.…”