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Introduction to reservoir/excess pressure

The Reservoir-wave hypothesis states that it is convenient to separate the arterial pressure into a reservoir pressure, that accounts for the energy stored by the elastic walls of the arterial system during systole and released during diastole, and an excess pressure, defined as the difference between the measured arterial pressure and the reservoir pressure.

P = Pres + Pex

In our original statement of the hypothesis Wang et al. (2003) we called the 'reservoir' pressure the 'Windkessel' pressure because of its close resemblance to the Windkessel pressure first introduced by Borelli (1680), popularised by Hales (1734) and made quantitative by Frank (1899). As our ideas developed, we realised that there were subtle differences between the reservoir pressure and the Windkessel pressure and so introduced the term 'reservoir' pressure Wang et al (2005). Unfortunately, at the time we also thought that the excess pressure was responsible for all of the waves in the arterial system and renamed the 'excess' pressure to the the 'wave' pressure. We now realise that waves are also involved in the development of the reservoir pressure, a notion that is implicitly denied in the 'wave' pressure terminology, and so we now prefer to call the two components the 'reservoir' and the 'excess' pressure.

The best way to introduce the reservoir/excess pressure concept is with an example.

 

[image]

The figure shows the measured pressure (black) in the human ascending aorta, the reservoir pressure (green) calculated as detailed below and the excess pressure (blue) calculated as the difference. All of the pressures are shown relative to their initial value so that the different components can be compared directly.

Several features of the separation can be seen immediately. The reservoir pressure matches the measured pressure very closely during the latter stages of diastole. In early systole the reservoir pressure 'lags' behind the excess pressure and, in fact, continues to decrease slightly during very early systole. As a result of this, the excess pressure is very similar to the measured pressure during early systole but is very close to zero during diastole.

The reasons for these features of the separated pressures will be discussed in detail in later pages, together with their implications.

The following pages are arranged roughly in the following way. The purpose of these reservoir/excess pressure pages is less pedagogical than the companion Introduction to Wave Intensity Analysis and so it should be possible to start almost anywhere. I will try to make links between the different sections to make it easier to navigate through all of the different topics.

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