Huygens' Principle geometric derivation and elimination of the wake and backward wave

Huygens' Principle (1678) implies that every point on a wave front serves as a source of secondary wavelets, and the new wave front is the tangential surface to all the secondary wavelets. But two problems arise: portions of wavelets that exist outside of the new wave front combine to form a wake. Also there are two tangential surfaces so wave fronts are propagated in both the forward and backward directions. These problems have not previously been resolved by using a geometrical theory with impulsive wavelets that are in harmony with Huygens' geometrical description. Doing so would provide deeper understanding of and greater intuition into wave propagation, in addition to providing a new model for wave propagation analysis. The interpretation, developed here, of Huygens' geometrical construction shows Huygens' Principle to be correct: as for the wake, the Huygens' wavelets disappear when combined except where they contact their common tangent surfaces, the new propagating wave fronts. As for the backward wave, a source propagates both a forward wave and a backward wave when it is stationary, but it propagates only the forward wave front when it is advancing with a speed equal to the propagation speed of the wave fronts.

Localization of Arterial Bleeds Using Pulse Wave Reflections

ABSTRACT Introduction Localization of internal arterial bleeds is necessary for treatment in the battlefield. In this article, we describe a novel approach that utilizes pulse wave reflections generated by a bleed to locate it. Materials and Methods To demonstrate our approach, velocity and diameter waveforms in the presence of bleeds were simulated using the 1D wave propagation equations in a straight-vessel model of the human thoracic aorta. The simulated waveforms were then decomposed into forward and backward components using wave intensity analysis. Reflections arising from the bleed were identified from the decomposed waveforms. Results Reflection generated by the bleed introduced a new feature in the backward component, compared to the normal, no-bleed condition. The bleed location could be determined from the time delay between this reflection feature and the forward wave creating it, and the pulse wave velocity in the vessel. Conclusions The findings of this study could be utilized by ultrasound for hemorrhage localization.

Acute effects of transcatheter aortic valve replacement on the ventricular-aortic interaction

Transcatheter aortic valve replacement (TAVR) is linked with an immediate increase in aortic systolic blood pressure and maximal flow, as well as steeper aortic pressure and flow wave upstrokes. After TAVR, the forward wave pumped by the heart is enhanced. Although the arterial properties remain unchanged, the central augmentation index (AIx) is markedly decreased after TAVR. This challenges the interpretation of AIx as a solely vascular measure in patients with aortic valve stenosis.