A primer on passive electrodes.



Abstract


We argue that if any heart pacemaker is going to be implanted at all, the device better go for the gold and and besides pacing, also control, in time and space, the propagation of the ions through the heart muscle, in order to control the heart's squeezing sequence. Note the subtlety here that while most electric currents propagate through the fixed path of the wires, the electric currents in the heart muscle is a 3-D (3-dimentional) propagation which we call vector current . Moreover, as the heart tissue resistivity changes as the person ages and suffers a sequence of broken heart events, so does the current propagation reorganizes and consequently the squeezing sequence also reorganizes. The consequence of this continuous change of resistivity of the heart muscle is the variation of what the cardio people call the ejection fraction (EF), which is defined as the volumetric fraction of blood that is pumped forward at each contraction cycle. This turns out to be a amazingly small number: 75% for an Olympics athlete, 70% for a young person in optimal physical shape, then down from there. No engineer would keep his/her job if he designed such a dismal pump.

We then introduce what we call passive electrodes , which are electrically insulated electrodes, able to project an electric field in their neighborhood, but unable to inject electric currents in the heart muscle. This electric field created by the passive electrodes does, in turn, apply a force (Coulomb's law) on the propagating ions, therefore controlling the path and speed of the ions that cause the muscle contraction. Ordinary electrodes cannot be used to control the vector current because they would also inject electric charges, which is not allowed to go continuously in the heart. Passive electrodes, on the other hand, can be used to control the vector current at all times because they DO NOT inject charges in the heart muscle so they can be on continuously. We argue that with the passive electrodes it is possible to correct for heart defects as "... faulty electrical pathway [at] sections of the hearts of those who are prone to developing cardiac arrhythmias such as atrial fibrillation, atrial flutter, supraventricular tachycardias (SVT) and Wolff-Parkinson-White syndrome." (from Wikipedia, 150801). We also argue that it is possible to correct for heart blocking too. We finally suggest that it may be possible to increase the heart ejection fraction (EF) from its best at even an earlier age, because the passive electrodes control the progressive heart muscle contraction, therefore changing the heart contraction sequence towards the ideal peristaltic pump. We finally suggest that the heart was not a consequence of the American "intelligent design", and that if anything it is a very poor design that can be corrected by the passive electrodes.

Introduction


A missing piece in the development of a better heart pacemaker is the control of the motion of the injected charges (ions) at the position x ( t ) as they propagate through the heart muscle. Elementary mechanics teach us that this could be achieved with a suitable electric field E following the chain:

x ( t > to ) = x ( x o , v, a, t )

v = v ( a, t )

a = a ( F, t)

F = F ( E, t),

where we are using the usual conventions of boldface to indicate vector, x = (x1, x2, x3) for spacial position in some arbitrary coordinates (x1, x2, x3), v for velocity, a for acceleration, F for force, E for electric field, and the repetition of the letter to indicate each new function, as in v ( a ) instead of f ( a ) for function of a. The bottom line of this is that if one were to control the value of the electric field E over the heart muscle, one would be able to control the speed and direction of the ions that cause the muscle contraction. (Off the record: This said, we are aware that the situation in the heart is more complex than this simple-minded initial approach due to ions of different polarity, of dipoles and etc.)

Some of the heart problems that may be ameliorated or solved
with the passive electrode method


One example of the heart problems that this technique of acting on the propagating ions as they move through the heart may solve is the phrenic nerve capture. The phrenic nerve capture is the consequence of electric charges escaping from the heart then entering the nearby phrenic nerve. If then a large enough current escapes the heart muscle and enters the phrenic nerve, which passes next to the left ventricle, this may, in turn, cause that the phrenic nerve, like any other nerve in our body, propagates the electric signal, delivering the electric signal to its termination point, which is the diaphragm muscle. If the electric current is high enough it may cause undesirable movements of the diaphragm muscle. This is sometimes strong enough that one of the electrodes used in cardiac resynchronization therapy has to be disconnected (when the problem cannot be solved by, e.g., decreasing the electric potential of the electrode). I do not know how often this happens but I know that it does happen, it having been told me by a cardiologist I trust. I also do not know if indeed the cardiologist succeeds sometimes in solving the problem simply decreasing the electric potential at the offending electrode, usually the third electrode at the left ventricle — I just guess because this is too obvious. Do you know how often?, then please tell me. Do you know if the cardiologists can sometimes salve the situation by decreasing the electric potential of the electrode at the left ventricle?, then please tell me.

Another example of the heart problems that this technique of applying an electric field at the heart location may solve is what is know as atrial ventricular blocking. It appears that the conduction of the electric pulse that causes the heart contraction sequence is sometimes blocked, ultimately preventing the contraction of the ventricles. I am not sure of the details of this because I am a physicist, not a cardiologist. It seems that one of the solutions used today is what the cardiologists call microwave ablation, a process that consists of inserting an electrode through a convenient vein (apparently from the groin), then advancing an electrode through the vein into the heart, then ablating some regions in the inner heart wall ( i.e., zapping them!), which causes scar tissue. As a physicist I interpret this as a method to change the resistivity of the heart muscle, which then redirects the path of the propagating ions. This method has the disadvantage of being irreversible, as once the cells are destroyed they cannot be " un-destroyed ". If instead, one were to apply a force on the propagating ions (with an externally created electric field E), it is expectable that a similar effect of redirecting the path of the propagating ions would ensue — at least it seems so to me, as a physicist. From my readings on the subject it seems that there exists a full set of heart problems that are related to the conductivity of the heart tissues, as atrial flutter and more, which ought to be at least ameliorated, if not solved with the method I am proposing.

Another problem that can be addressed by the technique we propose below, is the problem of the pumping efficiency. This problem has never been addressed or even considered before. Overall, this technique of applying a local force on the propagating ions, as they move through the heart muscle, ought to improve the heart pumping efficiency because a good contraction sequence ought to be associated with a good pumping efficiency. It seems to me that the cardiologists are not attuned to what I take as a fact, that the heart pumps sequentially, the cells contracting in a sequence, one after the other, and not instantaneously. Hard as it is to believe, it seems to me that the cardiologists think that all the heart cells contract together at the same time. This sequential contraction is fast for the human eye to perceive (on the order of 10s to 100s ms), but still a sequential contraction. It seems to me that when the cardiologists talk about sequential contraction they only mean that the atrium contracts before the ventricle, and not that each of them contracts sequentially towards the exit port, as any peristaltic pump does, the atrium contracting downwards for a lower exit into the ventricle below it, and the ventricle contracting upwards, for an upper exit into the pulmonary and the aorta arteries above it. This said, we are aware of the consequence of the Purkinjie fibers on the ventricular contraction. (this is off the record too... ☺ )

Previous work


Ablation is primitive medicine .
Rob Dunn "The Man Who Touched His Own Heart" pg. 5

As an analogy, what I am proposing is akin to what the French neurosurgeon Benabid (1987) did in 1987 for Parkinson's disease surgery. Back then, the neurosurgeon did zap neurons at the lower part of the brain (say, the STN, GPi, etc.), much as the cardiologists today zap the inner heart wall to solve the electrical conduction problems in the heart. The cardiologists euphemistically call it catheter ablation ref 1, wikipedia and particularly, for more details ref 2, Brigham and Women's Hospital ). When Benabid discovered that simply applying a low voltage 200 Hz pulse at the region that it was previously destroyed would also stop the Parkinson's tremor, the old zapping (to avoid their ablation euphemism) was abandoned in favor of the current technique that is known as Deep Brain Stimulation (DBS). DBS consists of implanting an electrode deep at the base of the brain (the reason for its name), which is involved in the tremor, then connecting the electrode to a battery and associated controlling electronics, which then keeps injecting a 200 Hz in that particular part of the brain. Benabid taught the world that exciting the neural cells at a frequency of around 200 Hz cause the cells to stop the misfiring that created the Parkinson's disease tremor, which is preferable to destroy these cells. A similar advantage is true for the heart: instead of zapping the heart to create scar tissue to cause a redirection of the electrical pathway to control conduction problems, one would do better with a reversible method of controlling the motion of the propagating ions instead of destroying heart tissue . But keep in mind that the similarity is valid only to the extent of avoiding ablation. Also, this new method to solve the problems of electrical conduction through the heart is but one of the applications of the passive electrodes and the general method of creating some desirable electric field E that I am proposing.

and as in other matters, delendum est ablation

Implanting a heart pacemaker


This is now a good time for the reader to become aware of how the electrodes for the artificial heart pacemaker are implanted in the heart. The artificial heart pacemaker is NOT implanted with open heart surgery, the chest is NOT cut open, but rather with a most simple surgery that involves a 5 cm long, 1 cm deep cut just below the clavicle (collar bone), to reach the sub-clavian vein. The wire with the electrodes is then inserted through this vein (occasionally from other vein too), in a procedure that from there on is not much more traumatic than inserting a needle to take blood from one's arm. The heart pacemaker surgery involves virtually no blood (though I had to close my eyes when I saw a real video of one, and so will you if you are a physicist, or a mathematician, or an engineer). This animation shows the procedure, and I can watch it, so I believe you can too; it is just an animation, not a video of an actual procedure.

                                                 

Hardware description


Given that forcing an externally created electric field to cajole the ions to go here and there is such an obvious thing to do, a mature person will wonder if it was never tried before, and if it was, why it is not used — perhaps it did not work for some reason? Perhaps this sequential reasoning has not been pursued because, though the stimulating electrodes acting in artificial heart pacemaking do create an electric field in the surrounding space, and therefore act on the injected charges to guide them after they are released in the heart muscle, they are " on " for a very very short time — a condition that cannot be changed because the heart would not pump if the stimulating electrodes were to inject charges in the muscle continuously! Perhaps the method was abandoned at the bud because it does not work with the stimulating electrodes, the ones I call active electrodes, and the method cannot indeed be applied with the active electrodes. But wait a minute: how about an extra set of (electrically) insulated electrodes? An electrically insulated electrode would not inject electric charges , yet would be perfectly capable of creating an electric field in the space around it! We call such electrodes passive electrodes, because they are passive insofar as not being active on the injection of electric charges, the function of the existing electrodes that we then call active electrodes.

Such an insulated electrode would never inject electric charges in its vicinity, so it could be on all the time. Then, again because such an insulated electrode would not participate in the injection of electric charges in the muscle, it could be set at any electric potential (voltage as the Americans say it). Moreover, because such an insulated electrode would not inject any electric charge, it could be physically located anywhere in the body.

I am here suggesting three options for the placement of the passive electrodes, as shown in figures 1, 2 and 3. The first row, 1a, 2a and 3a depict a drawing showing the important parts of the device, while the second row, 1b, 2b and 3b depict an artistic redention (1b) or an actual photo of the device (2b and 3b). Figures 1a and 1b show passive electrodes associated with the wires already used for the artificial heart pacemaker. Figures 2a and 2b show passive electrodes associated with a specially designed heart lining, as the lining created and used by LizhiXu, ... Igor R. Efimov et al. . Finally, figures 3a and 3b show passive electrodes associated with the Lara shirt, which is a shirt designed for the support of external passive electrodes covering the upper torso of the patient. Of course that other configurations for the passive electrodes are possible, and we hope that our colleagues will come with improvements on our suggestions and even completely new and inovative concepts.



The new problem is then where to put the new type of electrodes, the passive electrodes, with the objective of creating the best electric field in the volume of the heart muscle, with the natural constraints imposed by the required surgical procedure — when any is required. The electric field, in turn, should be such as to guide the injected charges to the best path that causes the best contraction sequence of the heart.



      Figure 1a - larger            Figure 2a - larger                   Figure 3a - larger

       

      Figure 1b - larger                 Figure 2b - larger                Figure 3b - larger
                                       Nature Comm Vol 5 Pg 3329 (2014)
                                       This is a real picture of the heart
                                       of a former unfortunate rabbit.
                                       You really should read the articles,
                                       refs 1, 2 and 3.

The position of the passive electrodes is easy to find, the guiding principles coming from mathematics, from the equations that define the electric potential V, or from the equations that define the electric field E . The solution of the Poisson equation, which is the equation that governs the electric potential V, requires one of two boundary conditions, which are either the Dirichlet or the Neumann boundary conditions (see below). Dirichlet's boundary condition specifies the value of the electric potential V at the boundary, and Neumann boundary condition specifies the derivative of the electric potential dV / dx at the boundary. This latter, the boundary, is a surface that completely encloses the volume in question. The volume would then be the heart. Consequently, mathematics determine the position of the passive electrodes: the passive electrodes should completely fill a closed surface that encloses the heart. This mathematical best is difficult to implement, though, and some compromises may need to be made. The mathematics that describes the problem, and some of the compromises that we believe are required are discussed below. The compromises we discuss are, quite naturally, within the three possible configurations that we present, many more being possible to devise, and we hope they will be.

Introduction to the mathematics that define the problem


Mathematically this problem has traditionally been analyzed from the point of view of the electric potential V with a fixed electric electric potential V( x ) at the boundary. Several people have calculated the electric potential for the brain electrodes, e.g., Butson and McIntyre (2006) and Buhlmann et al. (2011) . I am sure that a lot has been done for the heart too, but I am just entering the heart problem and am unfamiliar with its literature. I know of CHASTE, a good platform for heart simulations developed at Oxford University, which has a strong user community, but I have not yet used it.

If one were to solve this problem the way it was solved for the brain, as per Butson and McIntyre (2006) and Buhlmann et al. (2011) above, then one would be dealing with a Poisson's equation

Δ (V) = - ρ / ε , where Δ is the Laplacian operator, ρ is the electric charge density and ε is the permitivity of the medium.

To complete the solution of the above differential equation one would either use Dirichlet's boundary condition (known electric potential at the boundary) or Neumann's boundary condition (the derivative of the electric potential at the boundary). This latter, the Neumann's boundary condition, happens to physically be the specification of the electric charges at the boundary, because

δ V / δ n = - En = - σ s / ε,

where δ stands for partial derivative (I have limited symbols here) and n is the normal to the surface and σ s is the electrical surface charge density.

So, the solution to Poisson equation requires the specification of one of the two boundary conditions on a surface S that completely encloses the region of interest: (1) the electric potential V or (2) the electric charge σ s (or the normal derivative of the electric potential δV / δn ). Note that both Dirichlet and Neumann boundary condition require that the boundary (the surface S) completely encloses the volume of interest. In this case, even the LizhiXu, ... Igor R. Efimov et al. (2014) membrane (figure 2b) is not enough, because there ought to exist holes in the membrane for the arteries and veins. Nevertheless, Lara's first conjecture states that the degree of control of the function V inside the boundary with incomplete boundary conditions (an incomplete surface S that does not completely enclose the volume of interest) is a monotonic increasing function of the completeness of the extension of the boundary condition, that is, in pedestrian words, the more control of the values at the boundary, even if incomplete control, the more one can control the value of the function V inside the incomplete boundary.

Consequently, it follows from the Lara first conjecture that option 2 (shown in figure 2a and 2b) offers the most control, followed by option 3 (shown in figure 3) then option 1 (shown in figure 1) . Option 1 offers the least control of the electric field E, but since it is the easiest implementation, it probably ought to be implemented even if other methods were also implemented. Option 1 offers also the advantage of the closeness between the passive electrodes and the heart muscle. Option 1 would barely, if it does at all, increase the price of production of a heart pacemaker — though we believe that it would substantially increase the price to the patient, because this is how the companies work!

Each of the three options suggested above offers its advantages and its disadvantages. As for control of the of the electric field, and ultimately of the propagating ions and of the heart contraction sequence, option 1 (figure 1) offers the simplest implementation, as it does not require any new devices beyond a set of passive electrodes on the wires already in the patient for the heart pacemaker itself. Option 2 (figures 2a and 2b) is the most difficult to implement. Option 2 was built and actually used ex-vivo on a rabbit's heart, offering the almost ideal solution — though not ideal for the rabbit, of course! (see references 1, 2 and 3). Option 2 offers the most control of the electric field in the heart, and therefore more control on the motion of the ions moving through the heart muscle, but at the cost of a most complex surgery, even if it could conceivable be made with laparoscopy. Finally, option 3 is motivated by the advantage of avoiding surgery: external passive electrodes. Option 3 offers a fairly large 3D angular cover of the heart (better control on the boundary conditions) while requiring no surgery. Recapitulating, option 1 offers the weakest control on the electric field E, but requires no new invasive elements, option 2 offers the strongest control on the electric field E, but requires a fairly invasive procedure, while option 3 is intermediate in its capabilities of control of the electric field E while it requires no surgery at all.

The improvement we are proposing ends here: just a method to control the electric field E in the heart's muscle — with view of controlling the motion of the propagating ions that cause the cell contraction and subsequent heart pumping.

A method and a means to increase the electric field
created by the passive electrodes


Independently of the above considerations, the question of the magnitude of the force on the propagating ions should be addressed. Without entering in the detailed calculations, which I have not done yet, I am making a second proposal, a type of electrode that is capable of an increase of the electric field (and therefore an increase of the force on the ions) by three orders of magnitude (a factor of 1,000). Together with the passive electrodes, we are proposing the use of the technology of supercapacitors to implement the passive electrodes. Physically what the electronics engineers call supercapacitors are capacitors such that their plates are made with a hemongous porosity, which much increase their surface area and consequently their capacitance. The technology allows the manufacture of capacitors with capacitances of the order of several Farads, 1,000 times larger than the capacitance obtained with the best prior technology, that of electrolytic capacitors. Electrodes made with supercapacitor technology (one plate only), would store more electric charge than the existing electrodes, and it may be easier to calculate the electric field E directly from the definition of E as

E = ( 1 / ( 4 * π * ε) ) Σ i ( Qi / ri3 ) r

In one way or another, whether calculating the electric field from the electric potential (and this latter from Poisson equations and the boundary conditions), or from the direct definition of it, once the electric field is determined on the volume of the heart muscle one can calculate the forces and then the path of the ions as they propagate and cause the contractions of the cells and the heart.

References


(1) LizhiXu, ... Igor R. Efimov et al. "3D multifunctional intergumentary membranes for spatiotemporal cardiac measurements and stimulation across the entire epicardium" Nature Comm Vol 5 Pg 3329 (March 2014 ).

(2) Colleen Clancy and Yang Xiang "Wrapped around the heart" Nature Vol 507 pg 43 (6 March 2014) .

(3) Pierre Martin "Une membrane artificielle pour surveiller le coeur" La Recherche (1 Mai 2014) .

Benabid et al. "... Thalamotomy and [electric] stimulation ..." (in normal language: " ... zapping someone's else's brain neurons into oblivion vs. electrical stimulation ...") Appl. Neurophysiol. V 50 Pg 344 (1987)

Buhlmann et al. "Modeling ... desynchronizing deep brain stimulation" (2011) Frontiers Neuroeng. V.4 article 15 (Dec 2011).

Butson and McIntyre "Role of electrode design ... deep brain stimulation" (2006) J. Neural Eng V. 3 pg. 1 (2006).




















         

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