Blood hammer phenomenon in human aorta: Theory and modeling.

This paper contains the results of computing of a blood pressure and a flow speed in a human aorta in a diastolic phase of a heart cycle. The model is based on the one-dimensional flow approach. The blood hammer effect means abrupt increasing of pressure in a blood vessels due to the sharp changes in flow speed. The closing of aortic valve at the proto-diastole phase causes such blood hammer. We consider an aorta as a simple cylindrical conduit with elastic walls. The aortic valve and the bifurcation were located in the opposite ends of the conduit. The analysis of possible types of blood hammer effect in the "conduit-blood" system was performed. The lifelike initial and boundary conditions for the problem were proposed. We found a strong peak of pressure during the first third of diastole at the normal closure of the aortic valve. We observed the minor fluctuations of pressure in the later part of diastole too. Blood flow speed also has minor oscillations during the diastole. Such results are typical under the complete blood hammer effect condition. An abnormal long valve closure causes an incomplete blood hammer effect. In that case the calculated oscillations of the flow speed had higher intensity without strong pressure peak. The Fourier spectra of pressure fluctuations are located in the range of 16-87 Hz, that is nearby to known frequencies of the second heart sound produced by aortic valve.

A new age-related model for blood stroke volume.

BACKGROUND: A new computer model for systolic pulse waves within the cardiovascular system is presented. The emphasis was made on blood stroke volume (BS). The new waveform for pulse wave demands the re-computing of the BS. The authors showed the applicability of suggested model for arterial aging problem. METHODS: Suggested model is based on the well-known Korteweg-de Vries (KdV) equation. Instead of the common accepted solitary wave, the periodical cnoidal wave is used. Both waves are exact solutions of the KdV equation. The cnoidal waves are described by the Jacobi elliptic functions. Depending on a specific parameter called the elliptic module, m (0≤m≤1), these functions can be either harmonic or hyperbolic type. RESULTS: The explicit expression for the dimensionless BS was obtained. The dimensionless BS depends, as was found, on the elliptic module only. Dimensional analysis demonstrates the dimensionless BS has limited range of variation. This allows the direct estimation of elliptic module that turns out to be close but not exact equal to one. It is shown, that correct calculations of BS can not be done at m=1 (corresponds to simpler soliton model), and the periodicity of pulse waves has to be taken into consideration. CONCLUSIONS: Only the cnoidal model with the limited wavelength provides the correct computing of the BS. The natural bounds of dimensionless BS were found for the first time.