Understanding the Human Machine - A Primer for Bioengineering - Max E. Valentinuzzi

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a surface electrocardiogram of one of these specimens where the sequence mentioned above is easily seen: a small upward spike SV (sinus venosus electrical activity), a negative pulse signaling the atrial activity called P, a large positive ventricular spike R and the last (negative in this case) smoother T wave (Valentinuzzi, Hoff & Geddes, 1969). The meaning of all these components is explained in detail further down in the text.

Figure 2.28 demonstrates the same electrical cardiac components, also in the snake, this time recording also with needle skin electrodes and with a catheter inserted in the sinus venosus (Valentinuzzi & Hoff, 1970).

Figure 2.29 shows clearly the full electromechanical correlation of events. The animal was an anesthetized snake. The upper channel is the surface electrocardiogram while the second and third channels were recorded with a catheter introduced in the sinus venosus carrying electrodes and tubing connected to a sensitive pressure transducer. The amplitude of the SV signal in channel 2 is very small and it could be improved by moving the catheter, but at the expense of losing signal from the sinus pressure, thus, a compromise had to be reached. SV (the pacemaker) was followed by the sinus contraction (channel 3) reaching ap-

Figure 2.29. FULL ELECTROMECHANICAL CORRELATION OF CARDIAC EVENTS. The animal was an anesthetized snake Constrictor constrictor, a Brazilian boa. After Valentinuzzi (1969). See text for explanation.

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proximately a maximum of 1.5 cmH2O. Atrial activity P is seen in the first two channels just preceding atrial contraction, which is shown in channel 4 (atrial pressure recorded with a tubing inserted through the atrial wall). The lower channel is intraventricular pressure obtained with a catheter and another sensor. There is a clear build up right after the R wave. The first arrow in channel Ap indicates the beginning of atrial contraction. The second arrow probably corresponds to the closure of the A- V valve, while the peak of atrial pressure reflects the isometric ventricular contraction through the bulging back of the A-V valve. The wave before atrial contraction is an indication of the sinus venosus contraction (Valentinuzzi, 1969; Valentinuzzi & Hoff, 1970). Briefly stated, the electrical depolarization of each stage is the mandatory triggering signal for the mechanical contraction, which, in the end, builds the pressure up and propels blood.

2.2.2.3. Spread of excitation: the conduction system

As in any excitable tissue, the action potential (often referred to as the cardiac impulse) propagates to all the heart: from the pacemaker site throughout the whole SV, from the latter to the right atrium and just slightly later to the left atrium, it traverses the atrioventricular junction to proceed to the ventricular base, ventricular apex and all the ventricular mass. In each stage, we underline, once the whole mass is fully depolarized, the mechanical contraction takes place. Frogs, turtles and snakes, because of their low frequencies (between 20 and 50 per minute, depending on the temperature), permit an easy visual inspection in experimental open chest preparations so that the sequential sinus, atrial and ventricular contractions can be followed when, by picking up the ventricle with a pair of tweezers, the heart is lifted to look at its posterior face. The SV is dark blue, the atria tend to be dark bluish-red and the ventricle has a lighter red color (well, perception of colors may vary from observer to observer). Filling and emptying of the chambers change the colors, too.

Crocodiles and caimans are the highest herptiles in the zoological scale. The last ones to have sinus venosus and the first with a full septum and, hence, separated right and left ventricular chambers. Birds follow them and, as in mammals including man, the sinus venosus disappears as a contractile chamber. However, a residual piece of specialized tissue remains only showing spontaneous electrical activity. This is the cardiac pacemaker located at the sinoatrial node (or SA node), in mammals usually found at the junction of the superior vena cava with the right atrium. The electrical impulse propagates to a second node — the atrioventricu-

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lar node (or AV node) — via three internodal tracts (anterior, middle and posterior) proceeding, thereafter, through the conduction system formed by the bundle of His, its right branch, the common left branch, the left posterior and right anterior branches, the Purkinje fibers and, finally to reach the regular ventricular fibers which make up the main myocardial mass. The conduction system is a transmission line showing very little mechanical activity, almost none. Its main function is to provide a fast and smooth path for the depolarization wave to reach the contracting fibers.

The atrioventricular (AV) node lies on the right side of the partition that divides the atria, near the bottom of the right atrium. It is somewhat similar to the SA node because, under certain conditions, it may produce spontaneous electrical activity. We should add that any cardiac fiber is potentially able to develop spontaneous activity.

The velocity of propagation of the cardiac action potential varies enormously all throughout the heart, being as slow as 0.02 m/s at the AV node and as high as 4 to 5 m/s at fibers of the Purkinje type or of the so called false tendon. Definitely, the AV node small region introduces a significant delay in the overall conduction process that has important clinical consequences when it reaches certain levels.

Thus, the heart displays four important properties: excitability (ability to change its electrical condition), automaticity (ability to generate and maintain the electrical changes), propagability (ability to propagate the electrical change) and contractility (elicitited by the electrical change, ability to produce mechanical work).

Study subject: Concept of refractory period, in nerve, skeletal and cardiac muscle. Check in any textbook of physiology or search in INTERNET.

2.2.2.4. Concept of block

Figure 2.30 is a simplified schematic of the cardiac conduction system, as described above. Similar to the traffic in a road, the depolarization wave can be detained at any place in its transit through the system, as for example at the bundle of His (see mark) so producing a bundle block, common and worrisome condition. The block can also occur somewhat further down, say at the common left bundle branch (CLBB), which is also rather frequent, or at either the posterior or the anterior left branches, the two latter usually referred to as hemiblocks (see two other marks in Figure 2.30). Blocks may take place between the two nodes and, most likely, localized at the very AV node. However, they can be seen within

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SAN	Internodal Tracts
	His Bundle
	CLBB
	LPB
AVN	RBB	Purkinje

Fibers

LAB

Purkinje

Fibers

Figure 2.30. CONDUCTION SYSTEM AND CONCEPT OF BLOCK. This is a schematic of the conduction system. SAN and AVN represent, respectively, the sino atrial and the atrioventricular nodes. Cardiac depolarization spreads throughout the atrial mass to elicit its contraction but it has rapid highways, the three interatrial or internodal tracts, to reach AVN from SAN. The bundle of His stems at AVN, is short, and soon divides into the right bundle branch (RBB) and the common left bundle branch (CLBB) that, in turn, subdivides into the left posterior (LPB) and left anterior branches (LAB). Both bundle branches give off the Purkinje terminal fibers that penetrate finally into the ventricular mass, the real recipient of the electrical signal. Depolarization can be blocked at any place in the system, as for example the marked locations.

the myocardial mass, too (many times under the general name of intraventricular blocks). As a rule, the higher the level of the block, going from peripheral ventricular sites to the AV node, the more serious the clinical condition generated by the block.

Study subjects: Find out who His and Purkinje were. Find out what Stokes–Adams disease is. The latter was probably the strongest motivation, circa 1958–1960, for the development of an electronic implantable device, now a commonplace that has saved and prolonged millions of lives. What device is it?

2.2.2.5. The surface electrocardiogram (or ECG)

When electrodes, connected to an adequate amplifier and the latter to a recorder, are hooked to any place on the skin, a typically well-defined signal called electrocardiogram (ECG) is registered. Willem Einthoven, in The Netherlands, was the first (in 1903) to obtain a good, reliable and reproducible recording using, after his invention, the famous string galvanometer. He founded modern electrocardiography getting for his contributions the Nobel Prize in 1924. In fact, there were antecedents to this

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Figure 2.31. THE NORMAL SURFACE ECG. Human surface record at the standardized recording speed of 25 mm/s with the usual amplitude calibration of 10 mm/mV. Each little square represents 1mmx1mm. The three beats show a prominent spike, the QRS complex, followed by the smaller and smoother T-wave and preceded by the very small atrial P-wave. In this case, the rate was 68/min.

outstanding and longstanding apparatus, for it took decades to be displaced by the electronic electrocardiograph (after 1950). The capillary electrometer, for example, was one of its ingenious but not well-suited ancestors. It made up a nice piece of history in the development of cardiac electrical activity recording (Geddes and Hoff, 1961).

Figure 2.31 displays a human ECG recorded with surface electrodes. The first beat shows only a spike, the QRS complex, followed by the smaller and smoother T-wave. The other two beats are complete, with the short and also curved P-wave preceding the QRS complex. R is the tallest and steepest spike, Q is just a very small negative spike at the beginning of R and practically non-existent in this record, and S is the small negative projection at the end of R. Einthoven named these waves with these letters and they were accepted ever after.

Obviously, the origin of this triphasic signal (three components or waves, no relationship whatsoever with the triphasic system of electrical engineers) must be searched in the myocytes themselves. However, each cardiac cell produces an action potential with a waveform completely different than that shown in Figure 2.31. How can this be explained?

− Relationship to the action potential

A differential signal from two monophasic action potentials

One first and simple explanation makes use of the subtraction of two cardiac action potentials, slightly shifted in time, as if they were recorded with microelectrodes. Take for example any of the recordings shown in Figure 2.23 (say, the ventricular signal), redraw it on a piece of paper, redraw it once more below it but shifted a little to the right (as if delayed); thereafter, subtract point by point the latter from the former

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choosing an appropriate sampling interval, and a waveform resembling an ECG will be obtained. If the width of one of the action potentials is shortened or lengthened, the last ECG component (or T-wave) can be made either positive or negative. This would be the combination obtained from just two fibers (Geddes, 1972).

The two electrodes of a surface ECG produce the differential signal between one electrode with respect to the other. One of the electrodes (placed at point A) can be thought of as recording a compound monophasic signal similar in shape to the cardiac action potential but the result of many fibers, say m, while the other electrode (placed at point B) would be recording the result of n cells and delayed due to the propagation time between the two points. Hence, we can write,

m	r
ECG = ∑ V Bj	− ∑ V Ak	(2.58)
j =1	k =1

where the first summation reflects the result from one of the electrodes, say B, and the second summation represents the compound monophasic signal of the second electrode, A, while m and r are the number of fibers “seen” by the electrodes, respectively. Still, there are other fibers whose action potentials are not detected by any electrode due to unfavorable relative locations.

The student is urged to actually do the graphic exercise described above in order to get the feeling of how both, delay and width of two monophasic signals determine the shape of the resulting wave. When there is no delay and widths are exactly the same, the result is zero or a flat line. It must be underlined that each monophasic component is not a “pure” action potential of full fiber-like amplitude but the composition of many, m and r, respectively, slightly different signals (in amplitude, width and may be in delay too). This rationale is applicable to the sinus venosus in lower animals as it is also to the atrial and ventricular electrical activities. We learn immediately that always the upstroke (or depolarization) of the monophasic wave is associated with a short spike in the surface recording, while the return (or repolarization) of the former roughly coincides in time with a smaller and smoother wave of the latter.

A biphasic signal from an excitation wave

A single excitable fiber in resting state is electrically negative inside and positive outside (Figure 2.32). Two external electrodes located at points A and B, respectively, are connected to a recording system. Always, the

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Figure 2.32. GENESIS OF THE BIPHASIC ACTION POTENTIAL. A single excitable fiber in resting state is electrically negative inside and positive outside. Two external electrodes located at points A and B, respectively, are connected to a measuring system. Always, the result is the difference of potential between A and B. Since at rest the potential of A is equal to the potential of B, the difference is zero and the detector will not show a displacement of its indicator. Point C indicates another electrode position which, when paired with A, will always yield a zero signal, irrespective of the fiber resting or excitatory state.

result is the difference of potential between A and B. Since at rest the potential of A is equal to the potential of B, the difference is zero and the detector will not show a displacement of its indicator (needle, oscilloscope beam or whatever). When a depolarizing front moves from the left to the right, as it passes under electrode A, there is a reversal of polarity and, say, that an upward difference is recorded by the recording system. If the refractory period of the tissue is short and the distance AB is long enough, the excited front will soon be between the two electrodes so that again the difference of potential will be zero. Hence, the display will show a positive spike signaling full passage of depolarization under A. Thereafter, the front reaches electrode B and the system will detect a potential difference similar to the first one but downward, because now B is negative to A (and before A was negative to B) while the arrangement of the system was kept constant. As the front proceeds to the right, the potential difference between A and B returns back to zero for the fiber is again at rest. Our record shows then two spikes: the first is positive and marks the passage of excitation under A while the second is negative signaling passage under B.

The refractory period of cardiac tissue is very long (easily, 200 to 400 ms). Thus, and repeating the reasoning, when the excitation front reaches A, an upward deflection will be recorded, as in the previous case, but as

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the front proceeds to the right, since the refractory period is long, it will touch simultaneously both electrodes which will see only the negative side and, thus, will show a zero difference. Depolarization stretches from A to B so that you can draw a shaded area between both points in order to visualize the concept. Thus, the recorder will have written a positive spike representing depolarization. Repolarization is now to be expected, and there are two possibilities depending on the metabolic conditions of the tissue: either repolarization starts at A or at B. If it starts at A (first region to depolarize is the first region to repolarize), a second negative spike will be recorded. If it starts at B (first region to depolarize is the last to repolarize), a second positive spike will show up. The student is advised to work out this reasoning by drawing sequentially the different situations and thinking carefully about the resulting polarities and differences of potential. A more detailed step-by-step description of these events can be found in the traditional textbook of Leslie A. Geddes (1972).

Summarizing: When recording the electrical activity of cardiac tissue with a pair of surface electrodes, two waves will be displayed, the first one (always positive) indicating depolarization, the second (either positive or negative) signaling repolarization.

The last important concept that we can learn from Figure 2.32 is when the position of the electrodes is changed so that one is placed at A and the other at C. In other words, the electrodes axis is perpendicular to the fiber axis, either in the resting or in the excited state, the potential difference recorded by the system will always be zero. As corollary, when the electrodes axis, instead, is parallel to the propagation pathway, the signal is a maximum in amplitude.

The student is advised to carefully read the previous paragraphs (the two explanations relating cardiac action potentials with surface ECG) and think over their contents. They have, indeed, significant practical consequences in the understanding of the electrical heart activity.

The ECG as the second derivative of the membrane potential

Figure 2.33 depicts a simplified electric model of the fiber schematic presented in Figure 2.32. It accounts for the extracellular fluid resistance r2, the intracellular fluid resistance r1, and the membrane impedance Zm, all expressed per unit length. The junction (or node, in the electric circuit meaning), with a negative sign, is at potential V2 and represents the excited or depolarized region. The difference between V2 and V1 is the membrane potential at any time, Vm. Longitudinal currents i1 and i2,

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through the intracellular and extracellular fluid, respectively, are driven by the small potential gradients generated by the excited region, so that,

r1i1 = ∂V1 / ∂x	(2.59)
r2i2 = ∂V2 / ∂x	(2.60)

where x stands for distance along the fiber axis. In fact and more exactly, the three dimensional space should be considered, but for the sake of mathematical simplicity and without losing concept, we will stick to the single dimension x.

Taken the derivative on both sides of the above equations leads to,

	r (∂i / ∂x) = ∂2V / ∂x2
	1	1	1		(2.61)
	r (∂i		/ ∂x) = ∂2V	/ ∂x2
	2	2	2

Inspection of the electric analog easily shows that the current, im, across the membrane appears because of gradients of current along the outside and the inside. In mathematical terms,

im = −∂i1 / ∂x = ∂i2 / ∂x

(2.62)

The negative sign simply considers the opposite directions of the two longitudinal currents. Replacement of the latter in eqs. (2.61) yields,

−r i			= ∂2V		∂x2	(2.63)
	1 m			1
r i	m	= ∂2V		2	∂x2	(2.64)
2

I2
r2	V2
Vm	Zm im
r1	V1
I2

Figure 2.33. ELECTRIC ANALOG OF THE CARDIAC FIBER (see also Figure 2.32). Extracellular fluid resistance r2, intracellular fluid resistance r1, and membrane impedance Zm are expressed per unit length. The outside junction with a negative sign, at potential V2, represents the excited or depolarized region. The difference between V2 and V1 is the membrane Vm potential at any time. Currents i1 and i2 through the intracellular and extracellular fluid, respectively, are driven by the small potential gradients generated by the excited region. The lower side of the picture, where i1, r1, and V1, are located, stands for the inner part of the fiber.

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Subtracting the above eq. (2.64) from its mate (2.63) produces,
(r + r )i	m	= ∂2V	m	∂x2	(2.65)
1 2

It should be recalled that the membrane potential Vm at any instant, either at rest or during excitation, is the difference between V2 and V1, as defined above.

This result is per se quite interesting, for it relates in a direct and simple way the current through the membrane with its difference of potential across. As parameters, only the two extracellular and intracellular fluid resistances are involved, with low numerical values relative to the membrane impedance. The membrane potential intervenes with its second derivative with respect to space, but it also changes with time when the action potential is triggered and, very important and significant, is its propagation along the fiber. Thus, we ask assistance from electromagnetic theory borrowing its wave equation,

Vm = f [(t − x / c)]

(2.66)

In other words, the action potential is looked upon as a mathematically unknown function of time and space taken place at the excitable tissue and moving at speed c. The student should perhaps review the subject to remind that the general solution of the wave eq. (2.66) is well-known and usually written as,

∂2Vm ∂x 2 = (1 c 2 )(∂2Vm ∂t 2 )= (r1 +r2 )im

(2.67)

Expression (2.67) is the differential form of the wave equation. Its last right portion only applies to the particular excitable fiber herein discussed. The mathematical description of the membrane potential change is not explicitly known, but it can be experimentally recorded and there are numerical approximations of different types. In fact, the latter still is a matter of study undertaken by many concerned electrophysiologists.

If the two right hand parts of eq. (2.67) are now considered, solving for the membrane current leads to,

	1		∂2V	∂2V
i =			m =K	m	(2.68)
m	c2(r	+r )	∂t2	∂t2
	1	2

and this reads as the membrane current being directly proportional to the second time derivative of the membrane potential, i.e., the action potential. A rather attractive concept because we can proceed one step further by saying that the surface ECG could be considered as proportional to the im and, hence,