Cleveland 12 Oct 98, Biomedical Engineering Society 15 minutes
Ann.Biomed.Eng. 26 (Supplement 1) S-16 (1998)
One in five of us will die just because the normal electrical rhythm of his healthy heart muscle flips to the alternative mode we call fibrillation.
This is the leading cause of death among adults. Those dying are not just couch potatoes eating MacDonalds. Among males of age 20-64, 1/3 of all deaths come from unexpected apparently spontaneous fibrillation, and a quarter of all those show no prior indication of anything wrong with the heart. The problem seems to be about dynamics, not about abnormalities. It seems that even in healthy hearts there are two alternative attractor basins. One is the usual sinus rhythm and the other is fibrillation. You can get to fibrillation more easily and more often in diseased hearts, but the existence of fibrillation has little to do with pathology. Since non-standard hearts are not yet describable physiologically, we scientists have to leave them to doctors while we try first to figure out the describable normal case.
One interesting feature of fibrillation is that the transition from V Tach to Fib in normal heart muscle seems to require a certain thickness of heart wall. This was first noticed in chemically excitable 3d media. If and only if the chemical gel has more than a certain threshold thickness, then a wave-breaking stimulus creates persistent wiggly vortex filaments within that thick layer. Activation fronts then circulate around the filament with a characteristic period. This period is far from perfectly regular. The theory of such things was clear enough 10 yrs ago that I could translate it into electrophysiological terms. The period should be around 100 msec and the critical thickness should be 4-5 mm. The dog heart wall is about twice that thick, and humans are somewhat thicker. Following this lead, five years ago Katherine Kavanagh's expts demonstrated a threshold thickness for fibrillation in normal dog hearts: it is 4-5 mm. And the characteristic period was around 100 msec.
Results like this encourage efforts to look more closely at fibrillating hearts with 3d explicitly in mind. For the past few years I've collaborated with Frank Witkowski at Edmonton, who built a new optical device for watching electrical activations on the dog heart. We look at the fluorescence of anepps dye in epicardial cell membranes during fibrillation. Here's how the experiments go that we published this March in Nature. (I have a dozen reprints here, and sample data on CDs)
This sleeping dog
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helped us with the experiments. She was rescued from the pound, de-wormed, fed well for the first time in a long while, groomed, and treated like a queen for a month ... and then put to sleep comfortably by injection of anesthetic. You see the respirator and the heating blanket here. We took out the heart
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into a pan of cold blood.
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Then working as quickly as possible while it's still cold we hitched it to a standard heart-lung support system that Frank's wife salvaged from throw-aways in the hospital operating room where she is a heart surgeon. Then we started pumping hot blood through it
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This kept it beating for 5 hours.
Meanwhile we filmed its activation patterns during episodes of fibrillation. To see the electrical activation patterns you inject the voltage-sensitive fluorescent dye into the aortic root. Heart cell membranes pick it up and turn purple. Then you turn on a bright turquoise light (500 +-40 nm), about 1/10 W/cm2.
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This is like sunlight cooled through water, not enough to damage membranes even after hours of exposure. It excites the dye to a faint orange fluorescence at 610 nm. This is no brighter than 10 microW/cm2. This is comparable to moonlight. And no more than 2% of this fluctuates in proportion to local membrane potential. If you can detect this fluctuation while filtering out the 10,000x brighter turquoise and the 100x greater background orange, and do this during 1 msec exposures, then the movie displays electrical activation waves at mm resolution. Two stages of image intensification achieve this for a cooled CCD camera.
Once every millisecond we snap a frame of 12-bit pixels 128 by128 each looking at about 1/4 mm2. This amplified photon count ends up as a digital number 0..4096 in each pixel represents about that same number of individual photons collected at the front lens. It is a very sensitive gadget, nearly at the physical limits. After a bunch of processing the S/N ratio is around 5. Details of how it works are in this March issue of CHAOS.
Here are 8000 frames of such imaging from 8 seconds of recording. I have a tall stack of these disks now from Frank. Then I write lots of C to analyze these movies on my unix workstation. Here is the sort of thing you see.
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Panel A here shows this very heart. This was our first experiments, 24 April last year. The field of view is about 5 cm square, as you see on the embalmed original heart here.The pacing electrode is here. (skip b) Panel C shows a wavefront moving out from it.
This wavefront would be elliptical in a 2d uniformly anisotropic medium, but this is a 3d heart wall with fibers rotating to perpendicular only a few mm below the surface.
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This rotating anisotropy introduces a characteristic squarishness to these "ellipses".
Then we strike with a 2nd impulse out of this bipole nearby. This is the scheme I proposed 15 years ago for such experiments. They weren't practical then and I couldn't get anyone to try them, but a few years later Ray Ideker made them work and created mirror image rotors just as planned. Panel D simply repeats that demonstration. You can see this onset of V Tach better in this slide
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The 2nd stimulus broke the ellipse, and its new free ends became rotors. They have about the 1 cm size and 100 ms period predicted.
(skip panels e, f,h)
back up the slide
Panel G shows their periodicity as activations on a map of distance vertically and time horizontally, where distance is along this white vertical line of sample points. Activations repeat at 115 msec intervals horizontally. The slope is the propagation speed, or anyway its projection along the white line. This is a pretty regular ventricular tachycardia with the chracteristic short period of rotors. How does it turn into fibrillation?
If it is just because of the short period, then a big pacing electrode fed V(t) recorded from fibrillation should induce fibrillation. If something about the geometry of activation fronts is essential, for example, the presence of rotors, then it won't. This experiment has still not been tried so far as I know.
The rotors are, of course, only surface manifestations of vortex filaments beneath the surface. The question now and the purpose of this experiment is to see what becomes of these filaments, after minutes of evolution.
In heart walls thicker than a vortex core diameter, which is about 4 mm transversely, these filaments go unstable somehow and you end up with the electrical turbulence called fibrillation. I proposed several possible modes of thickness-dependent filament instability in the Journal of Cardiovascular Electrophysiology in 1990. Fenton and Karma computationally found one more, published this year in the same issue of Chaos that I edited to focus on VF in normal VM. Here I gathered 19 papers from forefront experimentalists and theorists about fibrillation and defibrillation, and restricted the topic to physiologically normal ventricular muscle. This issue presents lots of good unsolved problems, if you are interested in solving such things.
In particular, even the simplest questions about vortex filament behavior in twisted anisotropic material remain to be answered. For example, how rapidly would fibers need to twist in depth so that the different anisotropies of all the layers would average out to isotropy? In this mouse, the heart is only 1 cm long. (pull it out from the pre-opened chest). Its left ventricular wall is only 1 mm thick, and the right ventricular free wall is only 1/4 mm thick. With a microsope you can see that the fibers show the usual counter-clockwise rotation from plane to plane into the thickness of the left wall, so fibers turn to perpendicular in just 1/2 mm of thickness. So is the mouse heart electrically isotropic despite its anatomical anisotropy? I don't know if anyone knows yet.
Another thing you might wonder is whether the period at which activation rotates around the vortex line depends on its orientation. There are basically 3 possible orientations:
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a) The first is Upright, running from epicardium to endocardium. Because it was convenient for observation and convenient for controlled stimulation of transverse activation fronts by a surface electrode, this is the way I designed the first expts to demonstrate ventricular rotors in dog heart. But starting from sinus rhythm rather than from an epicardial pacing electrode, the vortex filament naturally lies perpendicular to this.
So the filament is intramural, parallel to the surfaces. Then, depending on its depth or azimuthal orientation,
b) it can be parallel to fibers
c) or perpendicular to fibers.
Symmetry arguments indicate that the rotor period should be independent of filament orientation if the twist rate is slight. But it isn't slight, if you are working in animals smaller than whales. In dog or sheep you get a full rotation of fiber direction across the core of the vortex filament. We have no theory for an effect of orientation on rotation period. No one I have posed this problem to has solved it yet.
Note added to website a year later: see Berenfeld,O. and Pertsov,A.M. (1999) J.Theor.Biol. 199, 383-394 for solutions
You might also wonder whether the vortex line has any preferred orientation among these choices. Does it spontaneously move from one orientation to another, and settle there? Does the filament float to the intramural level of some preferred orientation? I suggested so in publications that are already 10 years old, but so far as I know there is no evidence yet one way or the other from real hearts or from computations.This seems mostly because the filament is subject to so many kinds of instability.
I've been speculating for an embarrassingly long time that these instabilities constitute the transition to VF. If that is so, Frank and I would like to know which one of the candidate instabilities does it. So far what we have seen on the dog heart surface is that a rotor spins for only several cycles before it's hit by waves at slightly shorter period, presumably from some other rotor, moving toward it. These impacts push the rotors outside the field of view while another often moves into the field of view. This is the sort of thing expected even in 2d theory and such 2d meander does produce an EKG that looks somewhat like fibrillation in 2 dimensional media. But most people would say it is more like torsade or some other tachycardia that typically precedes fibrillation. Its already 10 years since I suggested that torsade might be a moving vortex filament, so this is not too interesting today. But something interesting happens next.
After several minutes a qualitatively different pattern develops on the surface and the EKG then looks more like full-blown fibrillation. The period is still about the same, though. This suggests that the source mechanism is still the standard vortex line. But its period is now a bit shorter, as thought the filament were twisted, and less regular, as though the filament were moving around more freely. And surface patterns no longer look 2d.
If propagation were basically 2d, then the propagation speed should everywhere be nearly the same, after correcting for anisotropy. In Leon Glass' 1990 Theory of Heart symposium I showed this doesn't work in actual experiments, presumably because the anisotropy changes in the 3rd dimension: behind the epicardial plane the sheets of parallel fibers progressively twist.
But more importantly, if propagation is 3d, with activations coming from vortex filaments that worm around inside the wall, then you'd often see fronts asynchronously splatting into the surface from below. That might even be all you would see. The visible activation front is the moving intersection of a curved 3d wavefront where it hits the fluorescing epicardial surface, so you expect surface fluorescence patterns that move faster than physically possible propagation. They typically appear as a broad breakthrough area where the surface projection of the normal speed looks infinite at the point of initial tangency. This is just what we see.
Using an idea from Phil Bayly and Jack Rogers, my grad student Chen Gang wrote an IDL program to make contour maps of surface speed from these movie data so we can quantify this observation.
About one such breakthrough splat occurs per rotor period per unit surface area equal to a square wavelength. This amounts to about one per cm2 per sec on the epicardium.
Now if we integrate over the whole surface to make a clinical electrocardiogram, this behavior looks more like real fibrillation. Some people think its source is Purkinje fibers, functioning faster than they did during normal sinus rhythm. I feel that the period is too much a coincidence. I think its source is vortex filaments moving in the 3d thickness where it exceeds a rotor core diameter, like the models that Alain Karma and I have pursued.
We observe the characteristic period of vortex filaments, and we observe the expected splats onto the surface, and VT degrades to VF only when the threshold thickness predicted from such models is exceeded. But this evidence remains circumstantial until we can see what's going on inside.
I think I know a way to do this (go to omitted section on angles if there is time):
Imagine an activation front tilting into the epicardial surface. Three-dimensionally, it moves at a standard speed, depending on the local fiber direction. So its intersection with the surface is faster in proportion to the cosine of the angle of incidence. We infer the angle by observing that surface speed in relation to local fiber direction.Then we project that activation backward in time at that angle, at the speed corresponding to that direction, to see where it came from: maybe from intramural vortex filaments, or maybe not; maybe they come from Purkinje fibers: that is the more conventional expectation. Anyhow, the aim is to do this projection at every point on the surface. Using an idea from Phil Bayly and Jack Rogers, Chen Gang wrote an IDL program to make contour maps of surface speed from which we can obtain these angles. That is as far as we have got so far.
Thank you for listening.