23
Cardiac Pacing
Heart muscle | Striated muscle |
Target region is large | Limited target region |
Easy to avoid excitation of unwanted nerve | Excitable tissue to be avoided is close to target tissue |
In effect, all cells are similar in size and excitability | Fibers vary in diameter, questions there are concerning recruitment, order of recruitment, and order that can differ from normal |
Does not fatigue | Fatigue must be considered |
Pulse-on-T | Does not fibrillate |
Chamber paced | Chamber sensed | Response | Description of mechanism |
V A D V V A A V D |
0 0 0 V V A A A V |
0 0 0 I T I T T I |
Fixed-rate ventricular pacing Fixed-rate atrial pacing Fixed-rate AV pacing Ventricular sensing and pacing, inhibited mode Ventricular sensing and pacing, triggered mode Atrial sensing and pacing, inhibited mode Atrial sensing and pacing, triggered mode Atrial sensing, ventricular pacing, triggered mode Ventricular sensing, AV pacing, inhibited |
Fourth letter: rate modulation | Fifth letter: antiarrhythmia function | ||||||||||
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Note: First, second, third letters as in Table 23.2 Source: Bernstein, et al. (1987) |
(23.1) |
since the current leaving the electrode enters the interstitial space only. In fact, the boundary condition in the interstitial space is that the total current entering this space at r = a is the total applied current I_{a}. In view of Equation (23.1) and the definition of V_{m} then at r = a we have
(23.2) |
Consequently, the aforementioned boundary condition is
(23.3) |
where | = interstitial bidomain conductivity, as described in Equation 9.17 | |
I_{a} | = applied current, assumed to be cathodal (hence the minus sign) |
Now Equation 9.28 describes the behavior of V_{m} in the region r a under steady-state conditions (namely ). If this is substituted into Equation 23.3 and solved for the coefficient K_{A} we obtain
(23.4) |
Substituting this back into Equation 9.28 gives an expression for V_{m}, namely
(23.5) |
The maximum induced voltage is at r = a; in this case, Equation 23.5 reduces to V_{m max} or
(23.6) |
One notes from Equation 23.6 that the smaller the electrode the larger the induced voltage. For electrodes that are large compared with the space constant, the induced voltage varies inversely as the square of the electrode radius; but when the radius is much smaller than the space constant, the voltage varies only as the first power of the inverse radius.
With an endocardial lead the electrode is surrounded by cardiac tissue on one side and blood on the other. Since the blood conductivity is about three times greater than cardiac tissue, in our very simple isotropic model the applied current should possibly be reduced by some factor over what it would be in the assumed uniform model developed in Chapter 9 and extended above. We have chosen this factor to be around 35%. For a 1 ms stimulus pulse the membrane should come close to the assumed steady-state value (Cartee, 1991). Equation 23.6 gives the maximum steady-state induced voltage if we identify a as the equivalent radius of the (spherical) electrode. A fairly typical electrode has an area of 8.8 mm² (Breivik, Hoff, and Ohm, 1985). This is converted into a sphericalized radius of 1.2 mm as described in Miller et al. (1985). We also choose the space constant as λ = 0.5 mm (Plonsey and Barr, 1982), and assign (the interstitial conductivity as defined in Equation 9.17) the value of .002 S/cm. Then
V_{m max} = 34 · I_{a} | (23.7) |
where | I_{a} | = applied cathodal current [mA] |
V_{m max} | = membrane voltage [mV] |
If I_{a} is 0.44 mA, then V_{m} is 15.0 mV, which is not an unreasonable threshold voltage, considering the many approximations in this simple, homogeneous, isotropic model. The result is in the range of published measurements (Breivik, Hoff, and Ohm, 1985) and the empirical current threshold value of 0.05 mA/mm² (Tarjan, 1991). Based on Equation 23.6 the use of a smaller-sized electrode will diminish the required current for a given threshold transmembrane voltage, as noted above. There is a limit to the amount by which the electrode size can be decreased. The reason is that one has to reach the required threshold current with a fixed battery voltage, and this limits the maximum allowable circuit impedance. The latter, however, is mainly the electrode-tissue impedance, which increases inversely with the electrode radius. In a practical design one should also include the possible effect of growth of fibrous tissue around the electrode since this will increase the size of the effective radius a in Equation 23.6 (see Section 23.7). We note that in Equation 23.6, V_{m} is positive (depolarization) for an assumed cathodal (monopolar) electrode.
When the electrode is monopolar, the reference electrode is invariably chosen as the case of the pulse generator unit. The main advantage of the monopolar system is that only a single electrode wire (per chamber) has to be implanted. For endocardial leads this smaller size compared to a bipolar lead is clearly desirable. In addition, it also represents a smaller wire lying in the tricuspid valve, through which the catheter electrode must run. One of the disadvantages, though, is the presence of stimulating current throughout a large part of the thorax; thus striated muscles lying in this region may be stimulated, giving rise to annoying muscle twitch. Both the phrenic and diaphragmatic nerves have also been known to be affected.
The bipolar electrode has an electric field that varies as 1/r³ rather than 1/r² and, consequently, is less likely to affect excitable tissues remote from the site at which the electrodes have been placed. In addition, when these electrodes are used in the sensing mode, the bipolar configuration is less sensitive to interference from distant extraneous signals. Such electromagnetic interference may at times be mistaken for a cardiac signal and incorrect logical inferences drawn by a multiprogrammable pacemaker. With present technology the advantage of handling a single versus double wire per chamber is no longer very great. For more historical reasons unipolar systems are favored in the United States, whereas European systems favor bipolar.
2Li + I_{2} 2LiI | (23.8) |
Since no gas is produced, the lithium cell can be hermetically sealed. Furthermore the serious problem of breakdown of the separator in the zinc-mercury battery does not arise in the lithium-iodine cell since, in the latter, the separator forms spontaneously and is self-healing. The lithium battery also has a reliable end-of-life decay characteristic which fails slowly enough to permit its detection in a normal checkup and the scheduling of a timely replacement. In addition to these attractive features, the approximate 50% survival of the lithium-iodine battery is 12 years (Bernstein, 1991).
V_{m max} = 16.8 · I_{a} | (23.9) |
This amounts to a reduction in the stimulus strength by 2.0. In fact in experimental studies, one finds that the initial threshold at the time of placement of a ventricular pacing lead increases by factors of 2-4 over the following period (Miller et al., 1985).
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