Inaugural Lecture

Kim H. Parker

5 November 2002

For the benefit of many friends and colleagues who could not attend my Inaugural Lecture, I have decided to to make a web version. Transcribing the audio recording will take some time and so here is an outline version based upon the powerpoint visuals that I used. I do have a prepared version of my lecture, but on the night I departed so far from the 'script' that it is not very relevant. And so here is an outline of the slides that I used, you will have to use your imagination to provide what the words. Remember, 'be accessible and make it amusing'.

A brief technical note: A number of the slides use the custom animation facilities of powerpoint where you will need to use mouse clicks to see the custom animations. I also used a number of animations that did not survive the transformation of the powerpoint presentation to the web presentation. I have embedded them in this document at the appropriate place and they should work when you place the mouse over the frame. Please let me know if there are problems accessing this and I will try to sort them out.

Slides for my Inaugural Lecture

Title Slide: 'I want to assure you that the title appearing on the invitations and posters for my lecture is not an advertisement for our new undergraduate course on bioengineering -- dumbing down the subject in order to recruit more applicants -- it is really half a title reflecting, as you will hear, my personal experience in the subject.'

My Co-authors: Instead of trying to thank everyone -- a hopeless task -- I decided to simply list my co-authors over the years. The names are alphabetical except for two people that I would esecially like to thank: C.G. Caro, who founded the PFSU and has profoundly influenced by life, and C.P. Winlove, with whom I shared an office for 15 years and have written more than 50 papers. Without my co-authors, I could have done nothing in the field of bioengineering. 'If your name doesn't appear here, and you would like it to, please see me after the lecture.'

My Sponsers: Again the list is alphabetical except for the Clothworkers' Foundation, who I would like to thank specially, not only for personal support they provided me but particularly for their support for the study of bioengineering at Imperial College. I am sure that their influence in making bioengineering an institutional part of the college will be important for generations, if not centuries, to come. 'If your name doesn't appear here, and you would like it to, please see me after the lecture...'

A Brief CV: 'If you find this boring, Bob Dylan wrote a much more interesting CV for me which is on the left.'

I Aim at the Stars: Werner von Braun's autobiography provides a good illustration of the excitement that we felt during my postgraduate days working on rockets. Mort Sahl's subtitle helped keep our feet on the ground.

Views of the Saturn 7 Launch: Just a reminder of what we were doing and how complex the problems were.

Stephen Hales I: The start of a short history of arterial haemodynamics.

Stephen Hales II: The first mention of the Windkessel phenomenon.

Leonhard Euler I: 'I use this picture of Euler because everyone knows how seriously the Swiss take their money and so even if you don't know the almost transcendental influence of Euler in mathematics and mechanics you can get some feeling for his importance.

Leonhard Euler II: These are the equations that we still use to describe 1-D flow in arteries. 'My schoolboy latin does not allow me to interpret this for you accurately but I do recognise 'insuperabiles difficultates'. The rest can be paraphrased 'If God wanted us to understand blood flow in arteries, He would not have made the equations so difficult'.

Thomas Young: Young deduced the correct relationship for the wave speed in arteries using intuition and analogy to Newton's theory of the speed of sound. Despite many readings of both the lecture and the notes for the lecture, I still cannot follow his reasoning.

Bernhard Riemann: 'After nearly 100 years, God answered Euler's prayer, not by making the equations easier, but by giving us Riemann who introduced the method of characteristics, providing us with a general solutions of hyperbolic equations.

Otto Frank I: Probably the greatest quantitative physiologist who ever worked on the cardiovascular system.

Otto Frank II: He solved the Windkessel problem, suggested to him from his reading of Hales, and gave a mathematical derivation of the speed of sound in arteries that I can understand.

J.R. Womersley: Womersley solved the equations for flow in an elastic artery using an asymptotic analysis that led to a linear form of the equations that could be solved using Fourier decomposition methods. His linear solution has become the predominant way of looking at waves in arteries, found in all of the standard textbooks on haemodynamics.

Caro, Schroter and Fitzgerald: Just a brief reminder of why we are interested in arterial haemodynamics. 'Atherosclerosis will kill half of us here tonight.'

'The cardiovascular system is in steady state oscillation': 'This quote comes from a referee's report from our most recent, unpublished paper. It is a very prevalent view of the cardiovascular system and one that I would like to examine in this lecture.'

Fourier Analysis: The data on the left are the ECG and pressure in the main pulmonary artery, very typical of cardiovascular measurements. The apparent periodicity of the data suggest that Fourier analysis could be helpful. On the right is the Fourier analysis of the first three beats of the pressure data on the left. The fit, using only eight harmonics is extremely good. However, we should remember that this sort of decomposition can be done with any complete, orthogonal set of functions. Exact fits can be obtained using Bessel functions, Legendre polynomials or any one of an infinity of orthogonal functions. The fit obtained in the Fourier analysis does not necessarily mean that the observed signal is made up of sinusoidal wave trains.

'Blocked' Beats: This shows similar data from the same experiment when gaps occur due to the presence, quite spontaneous in this experiment, of blockage of the pacemaker signal. What we see is not the slowly diminishing periodic signal that we would expect to see in steady state oscillation when the driving force is removed, but the complete lack of 'periodic' signal during the gaps. This is typical of overdamped systems, and we know that over damped systems cannot be in steady state oscillation. This sort of behaviour is seen in another 'every day, household object' -- the machine gun. When the trigger is held down, a regular stream of bullets is produced. The instant the trigger is released, no bullets appear. We conclude that although regularity is necessary for steady state oscillation, regularity does not necessarily imply steady state oscillation.

Severn Bore I: Although most of the waves that we encounter are sinusoidal wave trains -- sound, light, etc. -- there are many examples of waves in nature that are not sinusoidal wave trains. The Severn Bore is one example.

Severn Bore II: This is a video downloaded from <www.severn-bore.com> showing the Severn Bore. Note the surfer on the left. Imagine how he or she feels, missing the wave and knowing that the next wave is 12 hours away.
Cadenza:A. Khir and M.J. Lever demonstrated the propagation of a single wave in an elastic string.
Method of Characteristics Solution: The method of characteristics devised by Riemann is a rather subtle and difficult bit of applied mathematics, but the results of the theory are remarkably simple.

Creating a Macroscopic Wave with a Succession of Incremental Wave Fronts: This animation shows how a succession of small, incremental wave fronts, both compressive (increasing pressure) and expansion (decreasing pressure), can be used to build up any waveform. In this case it is the pressure measured in the carotid artery. These small, incremental wave fronts, standard in the compressible gas dynamics used to design rocket nozzles, are the 'elemental' waves used in our theory of arterial waves.

The Four Types of Waves: We have to consider four different elemental waves: forward and backward, compressive and expansion waves.

Wave Intensity: Wave intensity is similar to acoustic intensity and describes the rate of energy flux due to the wave. It has the units of W/m²and has the convenient property that it is positive for forward waves and negative for backward waves. Also, the measured wave intensity is the algebraic sum of the wave intensities of the forward and backward waves that produce the measured waveform at any point.

Wave Intensity Measured in an Elderly Man: This is the wave intensity calculated from the pressure and velocity measured in the ascending aorta of an elderly patient undergoing peripheral vascular surgery at the Royal Brompton Hospital. Note the large positive wave intensity at the start of systole indicating the large compression wave generated by the contraction of the left ventricle. The large peak of positive wave intensity at the end of systole indicates that the slowing of flow in late systole is caused primarily by a forward expansion wave generated by the left ventricle as it starts to relax. Note also, the smaller negative peak in mid-systole that indicates the presence of a reflected wave in this patient.

The Effect of Aortic Occlusion of Wave Reflections: These are data obtained by A. Khir in the laboratories of J.V. Tyberg in Calgary. As the occlusions is moved towards the heart we see from the negative peak of wave intensity that the reflection is larger and earlier, very much as expected. What was not expected was the absence of any effect of the more distal occlusions.

PU-Loops: From the solution of the equations by the method of charateristics, we saw that the change in pressure and the change in velocity of a forward wave are linearly related and that the constant relating them is just the product of the density of blood, which we know, and the local wave speed, which we would like to measure. This means that during the earliest part of systole before there is time for the reflected waves to return to the site of measurement, a plot of pressure vs. velocity, the PU-loop, should be a straight line and that we can determine the wave speed from its slope. We see that this is the case, both in normal conditions and in the extreme case of the occlusion of the upper thoracic aorta seen in the previous slide.

Separation of Forward and Backward Waves: Knowing the local wave speed, the theory lets us separate the measured pressure and velocity into the forward and backward waves that produced the measured waveform. This has been done for the data for the previous slides. Note the large, self-canceling waves during diastole. Since we cannot think of anything that might be creating these waves physically, this is an unsatisfactory aspect of the theory and we conclude that they are being produced by the method of analysis, not the cardiovascular system.

Windkessel-Wave Hypothesis: This is part of our latest, still unpublished -- see slide 17 -- work. We suggest that the measured pressure can be thought of as a Windkessel component, varying in time but uniform throughout the arterial system, and the difference that we define as the excess pressure as is done in acoustics. We can obtain the parameters of the Windkessel model, the compiance of the arteries and the resistance of the microcirculation, by fitting the exponential fall in pressure predicted by the Frank solution to the measured pressure during diastole. When we do that, we can then use the measured flow into the arteries from the heart to predict the Windkessel pressure during systole. The difference between this and the measured pressure is the excess pressure. The bottom panel shows that the waveform of this excess pressure is remarkably similar to the measured flow waveform. These measurements were made by J-J. Wang and J.V. Tyberg in Calgary.

Excess Wave Intensity: To show that the correspondence between excess pressure and flow waveforms, which indicates that only forward waves are present in the ascending aorta, we made measurements when an intra-aortic balloon was placed in the abdominal aorta and inflated and deflated at a time so that the backward waves it generated arrived during systole. This shows excess wave intensity calculated for successive beats, one normal and one with the balloon active, showing the presence of the backward waves during balloon inflation.

A Model of the Systemic Arteries: I now turn to some of the applications of the wave intensity model and analysis that I have been involved with. First is a study done by J-J. Wang as part of his PhD studies with me using the method of characteristics to follow the waves generated by the heart and reflected by the resistance vessels at the periphery of this model of the arterial system based on the 55 largest arteries.

Model Predictions: This shows the pressure, velocities and transfer functions predicted from the model study at different locations in the arterial system. This work completely transformed my understanding of the mechanics of arterial flow. I now believe that it is the reflection and re-reflection of waves in the exremely complex, bifurcating tree of arteries that dictates most of the behaviour observed at different points of the arterial system.

Pressure as a Function of Distance along the Aorta: The complexity of the flow in the aorta is shown beautifully by these recent measurements by J-J. Wang and J.V. Tyberg in Calgary. This is the pressure waveform measured every 2 cm along the aorta from the ascending aorta to the femoral artery. Note how the peak pressure first falls and then increases and how the shape of the waveform changes continuously along the aorta.

The Intra-aortic Balloon: We are studying the mechanics of intra-aortic balloons as they are used as left ventricular assist devices in patients after cardiac surgery. Here we see how the inflation pattern of the balloon is affected by the hydrostatic pressure when the 'patient' sits up. This is work done by A. Khir, J.R. Pepper and D.G. Gibson at the Royal Brompton Hospital.
Non-invasive Measurement of Wave Intensity I: We are developing was to measure wave intensity non-invasively in the clinic at St. Mary's Hospital. This involves pressure measurements by aplanar tonometry and velocity measurements by Doppler ultrasound at palpable points in the arterial system; e.g. carotid, brachial, radial and femoral arteries. Since the measurements cannot be made simultaneously, we have to 'line up' sequential measurements using the ECG and, more recently, the linearity of the PU-loop in early systole. These are measurements taken in the carotid artery by A. Zambanini, S. Thom and A. Hughes at St. Mary's Hospital.

Non-invasive Measurement of Wave Intensity II: Prof. M. Sugawara of the Tokyo Women's Medical College has been a most valued collaborator from the start of my work on arterial haemodynamics. Recently, in collaboration with the Aloca Company, he has developed an ultrasound machine that measures the wall displacement using wall-tracking methods and blood velocity by Doppler simultaneously in the carotid artery. The results they are obtaining in clinical studies, particularly in the effects of valve repair, are fascinating and potentially important. I would also like to thank Prof. Sugawara for the tie that I am wearing tonight. 'How he knew that I would need a tie, I will never know?'

Coronary Artery Mechanics: The coronary artery is the holy grail of studies of arterial mechanics because of its clinical importance -- atherosclerosis in the coronaries is the primary cause of heart attacks. It is, however, the most difficult artery to study because the peripheral coronary vessels are embedded in the myocardium and so the contraction of the heart during systole effectively pumps flow in the coronaries from both ends. We see that coronary flow actually decreases during systole because of the compression of the peripheral coronary vessels. This is collaborative work with Prof. Tyberg's group in Calgary where we have made our first tentative steps into the complex world of coronary haemodynamics. Because wave intensity analysis is a temporal analysis, unlike the frequency based analysis of the methods based on Fourier analysis, we feel that it could be helpful in studying the both the magnitude and timing of the different waves that cause coronary flow.

Pulmonary Arterial Mechanics: A. O'Brien has been studying pulmonary arterial flow as part of her PhD research and the results are both interesting and potentially important clinically.. 'Unfortunately, her PhD examination is being held tomorrow and as both of her examiners are in the audience this evening, I do not want to prejudice the outcome of the examination by describing this brilliant, innovative research by a truly outstanding PhD student'.

Coda: I had planned to make a modest proposal for the conduct of the next RAE, but time did not allow.

Retinal Images I: This is the start of a brief description of some of the other work that I have been involved with over the years. Because of the shortness of time, I will have to be embarrassingly brief. This is work based on the PhD research of E. Martinez-Perez who looked at the analysis of retinal blood vessels from retinal images, such as this taken by M. Paresh at St. Mary's Hospital,

Retinal Images II: These are the blood vessels segmented from the original image using scale-space methods.

Retinal Images III: This shows the skeletons of the vessels with critical points marked; termini, bifurcations and crossings.

Retinal Images IV: This shows the arterial tree. From this image the computer also measures the geometrical properties of the vessels: diameter, lengths, branching angles, etc.

Retinal Images V: This shows the venous tree. Because entire vascular trees are obtained, it is also possible to calculate the topological properties and the current studies are relating these to diseases such as hypertension and diabetes.

Cartilage Mechanics I: This shows histological serial sections of cartilage, the surface (top) and middle regions (bottom). The sample on the left is stained for collagen and the one on the right is stained for proteoglycans. Note the difference in distributions, particularly in the pericellular region.

Cartilage Mechanics II: This very early measurement of cartilage deformation when force is applied to the surface by an 'indenter' is typical of all mechanical measurements of cartilage. Note particularly the very fast, almost instantaneous response followed by changes with a much longer time constant and, finally the slow creep of the material which, if the force was applied for a longer time, would carry on almost indefinately. Also notice that the pattern of deformation obtained obtained during loading and unloading of the sample are very different.

Cartilage Mechanics III: This shows some of the work Peter Winlove and I did in collaboration with A. Maroudas of the Technion on the osmotic pressure of cartilage. This is the osmotic pressure of glycosaminoglycan (GAG) solutions with equivalent fixed charge densities comparable to cartilage. The dots are experimental measurements and the lines are theoretical predictions based upon calculations of the electrostatic fields around the GAGs in the presence of different conentrations of free ions. Note that the ordinate is scaled in atmospheres and so the effects are large.

Cartilage Mechanics IV: This is an experiment that Peter Winlove and I have discussed doing for years. It is an attempt to explain the complex mechanical behaviour of cartilage from the behaviour of a simple GAG solution when a semipermeable membrane at the top of the beaker is loaded by a pressure P. This shows the equilibrium states before and after the load is applied. In the final loaded state, the pressure is balanced by the osmotic pressure generated when the GAG concentration reaches some critical concentration C_crit. 'Note that not only have I introduced a lot of GAGs into the lecture, but that they are also blue GAGs.'

Cartilage Mechanics V: This shows the intermediate steps after the load is applied. 1) initial equilibrium before the load is applied, 2) a rapid response while the concentration just under the membrane is less than C_crit when the rate of deformation is dictated by the permeability of the membrane, 3) a time when the concentration under the membrane first reaches C_crit when the applied pressure on the membrane and the osmotic pressure across the membrane are equal and so the movement of the membrane stops, 4) this is not an equilibrium state because the concentration gradient below the membrane means that the GAGs will diffuse away from the membrane lowering the concentration and the osmotic pressure so that the membrane can move, but with a time constant dictated by the diffusivity of the GAGs, and 5) the final equilibrium condition with the load present. The dynamics of unloading will depend upon the concentration gradients produced by the deformation and will be purely diffusion driven and so different from the dynamics during loading.

Red Blood Cell Mechanics I: With A. Diaz, a Marie Curie Fellow and in collaboration with W. Gratzer and J. Sleep from the Randall Centre at King's College London, Peter Winlove and I have been looking at the mechanics of the red blood cell. Red blood cells must deform greatly during their passage through the microcirculation. Also, the red blood cell membrane is not a simple lipid bilayer, but also involves a very complex membrane cytoskeleton. There are a large number of genetic diseases of the blood involving alterations in the cell membrane and cytoskeleton.

Red Blood Cell Mechanics II: The red blood cell has a characteristic bi-concave shape at rest. Our calculations show the deformation of an initially spherical cell when the volume of the cell is reduced, resulting in a shape very similar to that of the red blood cell. The parameter C in our theory is a non-dimensional number involving the ratio of the modulus describing the resistance of the membrane to shape changes within the plane of the membrane to the modulus describing the resistance to bending out of the plane of the membrane. C=0 corresponds to only a bending modulus.

C=0

C=0
Red Blood Cell Mechanics III: We have also done calculations to explain the results of experiments done on permeable red blood cell membranes using optical tweezers. The results of two experiments are shown on the left. On the right are two animations of the stretching of cells with low and high values of C.

C=0

C=1000
Red Blood Cell Mechanics IV: Most measurements of red cell membranes have been made using micropipette experiments where the membrane is deformed by suction applied to a micropipette applied to the surface of the cell. The left shows a tongue of membrane sucked into the pipette. On the right are two animations of suction into a pipette for C=100 and C=1000.

C=100

C=1000
Coda: I had also planned to make a few observations about the proposed merger with UCL, a very hot topic of discussion at the time of my lecture .

What is in a name?: My modest proposal for the name of the new, merged institution. the next RAE, but time did not allow.

Metabolic Modelling I: In collaboration with D.G. Johnston and colleages in Metabolic Medicine at St. Mary's Hospital, I have also been involved in modelling of metabolic processes in the body and would like to show just a couple of quick examples of how modelling can help in the understanding of clinical problems. The first is a study of glucose transport and utilisation between the mother and the fetus. The experiments were done using non-radioactive tracers in mothers with small for gestational age babies at the time of delivery in the hopes of understanding the mechanisms of this problem. The model is very simple in process engineering terms, but we think that it captures the essential behaviour of the mother-placenta-fetus system.

Metabolic Modelling II: Our experimental results showed concentrations at the time of delivery that could only be explained by the unsteady production of glucose by the placenta. The problem was that the human placenta had been shown not to contain any glucose 6 phosphatase, the enzyme essential to glucogenesis, and so this conclusion was untenable. After much debate, we finally published our conclusions and the next month a paper was published reporting the presence of glucose 6 phosphatase in the placenta. It seems that there are isoforms of the enzyme and that the previous experiments had used antibodies produced by one of the isoforms that isn't found in the placnta. '"Oh, don't believe any of my work published before 1997", was the refreshing response of the scientist responsible for the early studies who then went on to describe the complex systems of isoforms that she is now finding.'

Postprandial Thermogenesis: We have also looked at the metabolism of women who were normal but had developed diabetes during pregnancy -- an important group of subjects because they are 60% more likely to develop diabetes in later years and therefore need frequent testing. As can be seen, the data are very 'noisy' but with the model it has been possible to separate the normal from the gestational diabetic woman on the basis of the time constant of their response to a standard meal of carbohydrates, lipids and protein. 'For the past year I have had a 100% rate of success in classifying the subjects from my analysis of the data sent to me blindly until the most recent subject, a mother in her 40's who had developed gestational diabetes in her latest pregnancy but not in her two early pregnancies during her 20's, who I am sure was recruited simply to spoil my record of successes.'

Monochorionic Twin Placentas I: In collaboration with L. Wee and colleagues at Queen Charlotte's Hospital we have been looking at the vessels in the placenta of identical twins that share a single placenta. These twins are very much at risk because it is possible for the blood vessels of one twin to join the blood vessels of the other resulting in a transfusion of blood. We take these placentas after delivery and inject the arteries and veins using epoxy of different colours; red and yellow for the arteries and blue and green for the veins.

Monochorionic Twin Placentas II: This is a placenta after the epoxy has been injected but before the tissue has been removed by acid that dissolves the tissue but not the epoxy.

Monochorionic Twin Placentas III: This is our first cast. The lower right panel shows a region where 'yellow' arteries are connected to 'blue' veins of the other twin. Because of the high pressures in the artery, this type of connection means that blood will always flow from the 'yellow' twin, which would be fatal. However, in the upper right panel we see a connection between a 'red' artery and a 'yellow' artery through which blood could flow in either direction. This is probably how the yellow twin survived, I am pleased to say that both twins were delivered successfully and were very similar in size.

Monochorionic Twin Placentas IV: The Doppler signal measured in an artery-artery anastomosis shows a bi-directional velocity in the vessel. The velocity shows a 'beating' pattern that is characteristic of interference processes, undoubtedly due to the slight difference in the heart rate of the two fetuses.

Monochorionic Twin Placentas V: In our most recent cast we see in the bottom right panel an enormous region where 'red' arteries are feeding the 'green' veins of the other fetus, probably a third of the 'red' twins arterial flow is being transfused. Again in the top panel we see a very large vessel connecting a 'yellow' artery to a 'red' one. Our working hypothesis is that the size of the artery-artery anastomoses in surviving twins will be related to the area of arterial-venous anastomoses that are present.

Monochorionic Twin Placentas VI: This research takes on real significance with the emergence of a new technique involving the ablation of arteries on the surface of the placents by laser. Cutting an artery-artery connection could be fatal, but how does the surgeon, viewing the surface of the placenta through an endoscope and not having the advantage of vessels filled with different colours, decided which vessels to ablate?

Flea Jump: I would like to end with the very first work I did in the field of bioengineering -- filming the junp of the flea. The panel on the right shows the jump at normal camera framing rates -- the jump is too fast to be seen. On the right is an animation reconstructed from 6 frames of a film taken at 3500 frames/s which shows that the flea's legs have left the surface within 3 frames from the start of the jump. This corresponds to an acceleration of more than 100 times the acceleration due to gravity. Highly trained humans can only tolerate 10-15 G's.

Flea jump at 25 frames/s

Flea jump at 3500 frames/s
Thank You: