the justification of reservoir pressure

Before continuing with the theoretical development, we present some experimental evidence that the definition of the reservoir is reasonable. The data in the following figure were measured in the human aorta starting at the aortic root and then every 10 cm down the length of the aorta. Approximately 1 min of data were recorded at each measurement site and ensemble averaged using the R-wave of the ECG as the fiducial point.

Pressure relative to the R_wave

Pressure relative to the diastolic point

In the figure to the left, the data are plotted with time relative to the R-wave of the ECG. The solid lines are the measured ensemble averaged pressure and the dotted lines are the reservoir pressure calculated from the measured pressure. The pressure in the aortic root is black and the pressure for successive 10 cm intervals are plotted in progressively lighter gray. The propagation of the pressure pulse down the aorta is seen as a shifting of the pressure waveform to slightly later times. This time shift is the wave travel time. Note that the reservoir pressures calculated for the different measurement sites are similar, but shifted in time.

In the figure to the right, the same data are plotted relative to the diastolic point (the time of the minimum pressure just prior to the rapid rise of pressure marking the start of systole). The change of the pressure waveform down the aorta is easy to see in this format. Most importantly for our discussion, note how the reservoir pressures superimpose indicating that our definition of the reservoir pressure is experimentally reasonable.

Pressure (solid lines) measured in a human at 10 cm intervals from the aortic root to the femoral artery and the estimated reservoir pressure (dashed lines). t=0 is taken as the peak of the R-wave on the ECG. Note the propagation of the initial compression wave starting at about 100 ms which reaches the femoral artery about 180 ms. Also apparent is the forward decompression wave starting about 400 ms. The dicrotic notch evident in the more proximal measurements is seen as a little 'wiggle' in the pressure at about 450 ms.

The same data presented as a movie of the pressure as a function of distance: measured pressure (black), reservoir pressure (red), excess pressure (blue).

Forward travelling backward waves?

Prof. Tyberg presented some of their recent work at the recent Artery meeting in Verona. One of the slides that he showed provides the one of the best justifications for the reservoir-wave hypothesis. I hope to get copies of his figures coming from their dog experiments to show here, but for the time being am presenting the same analysis to our data measured in humans.

Pressure waveforms in the human aorta The pressure is measured in the ascending aorta and then every 10 cm down the aorta and the data are presented as pressure P vs. time t and distance x. The propagation of the pressure waveform is obvious by the delay in the foot of the initial compression wave as the measurement site moves downstream. The slope of the line connecting these points in the x-t plane is a direct measure of the wave speed.

Separated forward and backward pressure waveforms The In this plot P (black) is separated into its forward P+ (blue) and backward P- (red) components. This separation was done using the wave intensity formulation, but identical results would be obtained using impedance methods. It is obvious in the plot that the forward wave is propagating forward just like the measured pressure, but it also seems that the backward wave in also propagating forward. This raises very fundamental problems.

The reservoir and excess pressures This problem can be resolved by separating the measured pressure P into the reservoir pressure Pr and the excess pressure Px. We show the separation for the wave forms measured in the ascending aorta to the right.

Excess pressure waveforms in the human aorta This figure shows the Px calculated from P at each site down the aorta. Again we see that the excess pressure waveforms are propagating down the aorta.

Forward and backward excess pressure waveforms Separating Px (black) into its forward Px+ (blue) and backward Px- (red) components we see that Px+ is propagating forward and Px- is now propagating backward as it should be.

Because the backward excess pressure is relatively small and because of the noise in the human in vivo velocity measurements, The behaviour of P_x- is not as clear as it could be. The results from the dog experiments where the flow rate is measured by Transonic flow probes is much less noisy and the behaviour of the backward wave is very clear, it is possible to track the reflected wave all the way back to the ascending aorta and then follow its re-reflection from the closed aortic valve back down the aorta.

Other examples of measurements in the human aorta

Other examples of measurements made down the aorta are shown in the wave intensity pages (using the old assumption that the reservoir pressure was uniform throughout the arteries) 5.3 Examples of the reservoir pressure