Impedance and wave reflection in arterial system: simulation with geometrically tapered T-tubes

A review on low-dimensional physics-based models of systemic arteries: application to estimation of central aortic pressure

The physiological processes and mechanisms of an arterial system are complex and subtle. Physics-based models have been proven to be a very useful tool to simulate actual physiological behavior of the arteries. The current physics-based models include high-dimensional models (2D and 3D models) and low-dimensional models (0D, 1D and tube-load models). High-dimensional models can describe the local hemodynamic information of arteries in detail. With regard to an exact model of the whole arterial system, a high-dimensional model is computationally impracticable since the complex geometry, viscosity or elastic properties and complex vectorial output need to be provided. For low-dimensional models, the structure, centerline and viscosity or elastic properties only need to be provided. Therefore, low-dimensional modeling with lower computational costs might be a more applicable approach to represent hemodynamic properties of the entire arterial system and these three types of low-dimensional models have been extensively used in the study of cardiovascular dynamics. In recent decades, application of physics-based models to estimate central aortic pressure has attracted increasing interest. However, to our best knowledge, there has been few review paper about reconstruction of central aortic pressure using these physics-based models. In this paper, three types of low-dimensional physical models (0D, 1D and tube-load models) of systemic arteries are reviewed, the application of three types of models on estimation of central aortic pressure is taken as an example to discuss their advantages and disadvantages, and the proper choice of models for specific researches and applications are advised.

Exponential taper in arteries: an exact solution of its effect on blood flow velocity waveforms and impedance

The dimensions and wall elasticity commonly taper along the length of mammalian arteries. The effects of taper on flow velocity waveforms can be included by either of two methods; to theoretically divide the artery into short sections wherein the properties are assumed constant (the approximate solution); or to find an exact solution incorporating the effects of taper. In this paper, an exact solution to the resulting, and previously unsolved nonlinear Ricatti equation for the impedance, is obtained by a process of substitutions. This solution is utilised to develop an exact expression for the flow velocity in the artery. The transmission line equations are then combined into a single integral expression for the entire artery and an exact solution to this is evaluated. This is the first solution to simultaneously account for both geometric and elastic taper, and it has been validated by comparing simulations of flow in the aorta of a dog to those using an infinitesimal approximate solution. The Pulsatility Index of the approximate solution requires at least 10 segments to converge to within 5% of that using the exact solution. The exact solution thus accurately accounts for the effects of exponential taper, and may be used to improve existing arterial models, which use the less accurate and more computationally cumbersome approximate solution.

Viscoelasticity modulates resonance in the terminal aortic circulation

We used an inertance-viscoelastic windkessel model (IVW) to interpret aortic impedance patterns as seen in the terminal aortic circulation of the dog, and to explain evident oscillatory phenomena in flow measurements. This IVW model consists of an inertance, L, connected in series with a viscoelastic windkessel (VW) where the peripheral resistance, Rp, is connected in parallel with a Voigt cell (a resistor, Rd, in series with a capacitor, C) to account for viscoelasticity. Pressure and flow measurements were taken from the terminal aorta, just downstream of the origin of renal arteries, in three anaesthetised open-chest dogs, under a variety of haemodynamic conditions induced by administering a vasoconstrictor agent (methoxamine) and a vasodilator (sodium nitroprusside). Mean pressure ranged from 40 to 140 mm Hg. The resistance Rp was calculated as the ratio of mean pressure to mean flow. Parameters L, C and Rd were estimated by fitting measured to model predicted flow waves. We found that prominent oscillations observed in flow waves, from midsystole to diastole, are related to resonance that occurs at a frequency, f(o), where reactance of inertance of blood motion matches the reactance of arterial compliance. Estimates of f(o) increased from 2.4 to 10 Hz with increasing pressure and showed a correlation with values of static elastic moduli plotted against mean pressure of dogs' peripheral arteries previously reported by others. Viscous losses, Rd, of arterial wall motion limited the amplitude of resonance peak. We conclude that viscoelasticity, rather than pure elasticity, is a key issue to interpret terminal aortic impedance as it relates to resonance.