The technique has the advantage of being applied in the time domain and offers a straightforward and intuitive way to, at each moment in time and for a given location, understand the nature and direction of the waves present. Together with knowledge of the local wave speed, waves can be further decomposed into their respective forward and backward components. In the original formulation, temporal changes in local pressure ( dP) and flow velocity ( dU) are considered as wavefronts, and their product is the wave intensity, dI = dPdU, representing the energy flux carried by the wavefront. Ī more recently introduced technique (yet around the block now for about 30 years) for the analysis and interpretation of hemodynamics is wave intensity analysis (WIA). Pressure–volume loops have been and still are the solid gold standard basis of cardiac function assessment, yet the real functional information is only obtained when measurements are performed under altered loading conditions for assessment of functional indices such as the end-systolic pressure–volume relation or preload recruitable stroke work. Impedance analysis, based on pressure and flow(velocity), expands the notion of resistance (the ratio of mean pressure to mean flow) to pulsatile signals and allows us to assess the systemic or pulmonary circulation using a systems dynamics approach (in which one can either adopt a ‘windkessel’ or a wave-based paradigm for the interpretation). ![]() This has provided us with a toolkit of methods, techniques and paradigms that we use for the understanding of (components of) the cardiovascular system and the interaction between the heart and its arterial load. The above equation shows that the two sound waves having the same sound intensity but different frequencies have the same pressure amplitude.Much of our current understanding of cardiovascular physiology and hemodynamics, documented in seminal textbooks, is based on invasive measurements in mammals and in humans, with pressure and flow (velocity) – measured inside the heart or in the (ascending) aorta or pulmonary artery – and cardiac volumes being the key signals for our analyses. The change in volume is $\Delta V = (y_2 - y_1)A' = \Delta yA'$ and the initial volume is $V = \Delta x A'$. In our case consider that the volume decreases or the gas is compressed ($y_2 < y_1$) and the pressure increases. The volume of the gas decreases when $y_2 y_1$ (rarefaction). Figure 1 The pressure variations of a sinusoidal wave is sinusoidal. As the sound wave given by the wave function $y = A \cos (kx - \omega t)$ passes through the cylinder, the left end undergoes a displacement of $y_1$ and the right end undergoes a displacement of $y_2$ at time $t$. The left end of the cylinder is at $x$ and the right end is at $x \Delta x$ in our coordinate system. To express the sinusoidal pressure variations of a sound wave, we consider a cylindrical element of gas of length $\Delta x$ and cross-sectional area $A'$ as shown in Figure 1. ![]() You'll see that the pressure variations of a sinusoidal sound wave is again sinusoidal. ![]() The sound is better described in terms of its pressure variations than displacement variations. The sound wave travels in the form of successive compressions and rarefactions.
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