# An Introduction to Wave Intensity Analysis

### Kim H. Parker Department of Bioengineering Imperial College, London, UK

 The pressure waveform in the canine aorta. J.J. Wang University of Calgary Alberta, Canada.

Wave intensity analysis is now more than 20 years old. It offers an alternative to the traditional Fourier methods for the analysis of waves in blood vessels . It is based on very basic mechanical principles, the conservation of mass and momentum. The mathematics it uses, the method of characteristics, is rather complex but the results are remarkably simple.

This site is a very personal look at the subject. It involves many ideas and a lot of work from many others, students and colleagues, but the point of view is my own. This is particularly true of the notation which is rapidly evolving as the method is finding more and more applications clinically.

I hope that this site will provide a useful introduction to wave intensity analysis for newcomers to the field. I have tried to segregate the detailed mathematics so that it will be more accessible to non-mathematicians, but have included most of the mathematical detail (just click on the link labelled {mathematical details}). (Note that this link doesn't go anywhere, it just shows what the link looks like in the other pages.)

Eventually, it will contain programs and algorithms that can be used to analyse measured data. I also hope that it will stimulate other contributions and may eventually lead to a forum for users of wave intensity analysis.

### The reservoir-wave hypothesis

The reservoir-wave hypothesis grew out of our work on wave intensity analysis. It suggests that it is useful to separate the arterial pressure into a reservoir pressure accounting for the compliant nature of the arteries and an excess pressure accounting for local waves. The reservoir/excess pressure idea has generated a lot of very interesting work and is now the subject of its very own web pages (Reservoir/excess pressure). Some of the work is also contained in these pages, but there are many new developments, including a new, subtly different definition of the reservoir pressure. The link will open a new tab so that you can explore those pages without losing the link to these.

### Notes on Physiological Fluid Mechanics

Dr. Jennifer Siggers, Department of Bioengineering at Imperial College gave a short course on blood flow in an applied mathematics course organised by the University of L'Aquila and held in Alba Adiatica in September 2009. She has made her lecture notes available on-line. The lecture notes are an excellent introduction to cardiovascular fluid mechanics; complete, concise and very clear. They are highly recommended to anyone interested in the mathematical basis of the subject. Much of the material covered in these pages is included in these notes, pp.94-130, in a mathematically more rigorous form. (Jennifer Siggers, Physiological Fluid Mechanics).

### Service is resumed -- 06 September 2010

Our new server is now installed and linked to the web. I am sorry for the down time when my research pages were unavailable. Our server is no longer steam-driven and will, we hope, provide seamless access to the departmental research pages. There is a new address for my pages and so bookmarks should be updated.

### The reservoir--wave hypothesis -- new web pages

The reservoir-wave hypothesis which is discussed in these pages (see index) is an outgrowth of wave intensity analysis, but it has taken on a life of its own. To further discussion of the idea, I have written several pages on the reservoir/excess pressure model which may be of interest to readers of these pages.

Reservoir/excess Pressure web pages

Since the reservoir-wave hypothesis is less well-developed than wave intensity analysis, the style of the pages is less tutorial in form. The analysis is closely allied to the basic ideas of wave intensity analysis, but should stand on its own. There is a slightly new definition of reservoir pressure developed there and there are a number of examples of its use.

I would be happy to hear comments and suggestions for this site.

Kim H. Parker
k.parker@imperial.ac.uk