Pulse wave reflections in branching arterial networks and pulse diagnosis methods

Abstract

Wave propagation and reflection in the model of branching tree of viscoelastic cylindrical tubes filled with viscous fluid is considered when applied to pulse wave reflection in arterial networks. The dichotomous branching tree and the tree with two anastomoses between the second-order tubes are investigated. Influence of the geometrical and mechanical properties of the tree on the pulse wave propagation and spectral properties of the total admittance of the systems are investigated. It was found out that the admittance has a set of resonant harmonics. Any changes in parameters of microcirculatory bed and in blood rheology cause noticeable alterations of the amplitudes of resonant harmonics and negligible alterations of other harmonics. The set of resonant harmonics is independent of some variations in the tree geometry. The resonant properties of the models with and without anastomoses have some differences, that makes it possible to carry out the diagnosis of the state of inner organs with different types of vasculature. The results substantiate a possibility of the pulse diagnosis of inner organs' states by observing the amplitudes of the resonant harmonics only, without preliminary knowledge of individual structure of the real vascular bed of an inner organ.

Novel methods of pulse wave diagnostics based on compression of a superficial artery

“…The relationship d max = a · d b 0 , b ∼ 1 has been obtained for all the investigated vascular beds. The dependences d min /d 0 (ξ) and d max /d 0 (ξ) are close to the optimal relations d min /d 0 = ξ 1 + ξ 3 −1/3 and d max /d 0 = 1 + ξ 3 −1/3 predicted by Murray's law [3]. Wave reflection coefficient Γ ∼ 0 for the feeding artery and its branches whereas the big scatter −0.6 < Γ < 1 * Natalya Kizilova…”

“…The input wave admittance Y in = Q/P of the systemic tree and the intraorgan beds have been calculated. The corresponding numerical procedures for the tree-like models and the systems with anastomoses are based on pressure and flow continuity conditions in the vessel junctions [3].…”

“…It was shown that analysis of the P(U) curves, wave separation and wave intensity analysis give a useful tool for differential diagnostics of the wave reflection site (due to stenosis, atherosclerosis, occlusion) in the large intraorgan arteries and at the terminuses (microcirculatory level). Basing on the models and morphometric data the resonant harmonics of the intraorgan vasculatures [3,4] have been computed and the method is proposed for clinical diagnostics. The distributed models of the intraorgan vasculatures are preferable to be used as the terminal elements in the model of systemic arterial tree.…”

“…Determination of the diagnostically important parameters and their biomechanical interpretation are connected with mathematical approach to data analysis and solution of the corresponding coupling problem for the blood flow and vessel wall movement. Some novel aspects of the wave propagation in the arteries are connected with wave separation into the forward and backward running components, waveintensity analysis, estimation of the resonant harmonics, analysis of the pressure-flow P(U) curves and the curves dD/dt(D) have been recently studied in [2][3][4]. It was shown that negative wave reflection which amplifies the blood inflow due to the sucking effect is proper to the intraorgan vasculatures.…”

Optimal long‐distance transport systems in nature: control and applications (Poster Presentation)

“…P(t) and U(t) signals measured in healthy patients and calculated on the models of the intraorgan arterial beds have been compared and investigated using the wave-intensity analysis and wave separation technique: P (t) = P + (t) + P − (t) [1,2]. When P(t) signal is measured in the feeding artery of the organ the parameters of the forward wave are determined by the upstream conditions while the backward wave P − (t) carries information about the intraorgan circulation.…”