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The goal is to help create smooth energy-optimal monophasic pulse waveforms for defibrillation using the Luo-Rudy cardiomyocyte membrane computer model. The waveforms were described with the help of the piecewise linear function. Each line segment provides a transition from one present level of the transmembrane potential to the next with a minimal energy value. The duration of the last segment was defined as a minimum duration at which an action potential occurs. Monophasic waveforms of segments 3, 10 and 29 were built using different increments of the transmembrane potential. The pulse energy efficiency was evaluated according to their threshold energy ratios in mA
^{2}
·ms/cm
^{4}. There was virtually no difference between the threshold energy ratios of the three waveforms constructed and those of the previously studied energy-optimal half- sine waveform: 241 - 242 and 243 mA
^{2}
·ms/cm
^{4}. The pulse waveform constructed is characterized by a low rise and fall as the duration of the rise is ~1.5 times longer than that of the fall. Conclusion: Energy-optimal smooth monophasic pulse waveforms have the same threshold energy ratio as the optimal half-sine one which was studied before. The latter is equivalent to the first phase of biphasic quasisinusoidal Gurvich-Venin pulse which has been used in Russia since 1972. Thus, the use of the Luo-Rudy cardiomyocyte membrane model appears to offer no possibilities for a substantial increase in the energy efficiency (threshold energy ratio reduction) of the classical monophasic defibrillation pulse waveforms.

The world’s first monophasic pulse defibrillators (ID-1-VEI) began to be produced in the USSR in 1952 [

Thus, over the past 40 years, it has been possible to reduce the maximum energy defibrillator discharge which ensures a 95% - 100% success rate in the defibrillation/cardioversion of atrial and ventricular tachyarrhythmias, to as little as ~1.6 - 2 times (from 360 - 400 to about 200 joules). At the same time a significant decrease in the maximum discharge energy and current amplitude would be conducive to the solution of the following tasks:

・ To minimize/avoid myocardial damage/dysfunction, and tissue damage beneath the electrodes and related inflammatory processes, especially when applying repeated maximum energy discharges;

・ To alleviate painful sensations to enable external cardioversion without anesthetics by using only sedation in patients who are conscious;

・ To reduce defibrillator size and cost.

In physics, instantaneous electrical power of defibrillation pulse

Defibrillation pulse energy

Typical for adult transthoracic defibrillation are energy

Let us tentatively accept the value of transthoracic impedance as a constant value, so that it can be taken out of the integral (Equation (3)).

The integral of the square of the given current value of the defibrillation pulse will be called an energy pulse ratio^{2}∙s or W∙s/Ω (Equation (4)).

Since comparison of the energy efficiency of different defibrillation pulses should be made using the same value of transthoracic impedance, pulse energy efficiency may be indicated by its energy ratio

During an electric shock current extends in the chest in such a manner that a mere ~4% of its total quantity flows directly through the heart affecting its cardiomyocytes [

For the purposes of the study we used the guinea pig cardiomyocyte membrane model―1994-2000 Luo-Rudy mammalian ventricular model II (dynamic) which is part of the open source Cell Electrophysiology Simulation Environment (CESE) OSS 1.4.7 [^{2}. The segments of the piecewise linear function describing the energy-op- timal pulse waveforms were constructed by using energy-optimal trapezoidal segments (ramp), during which the transmembrane potential increases from the present level to the next, with the initial signal level of a subsequent segment being equal to the final signal level of the previous one. These segments are checked to determine the time required for the energy ratio to have a minimum value during the transition of the transmembrane potential from one predetermined level to another. Since exposure value in the model is not the current value, and its density, the dimension expressed in the energy ratio in the μA^{2}∙ms/cm^{4}. The last segment showed the minimum duration during which the action potential occurs. The threshold pulse energy ratio was defined as the sum of the energy ratios of its segments.

3 pulse were constructed using different numbers of segments:

・ 3-segment pulse (resting potential → 76 mV → 66 mV → action potential).

・ 10-segment pulse (resting potential → from 83 to 59 mV with a 3 mV increment → action potential).

・ 29-segment pulse (resting potential → from 85 to 58 mV with a 1 mV increment → action potential).

In constructing the pulse was convenient that their segments increased the transmembrane potential to an integer value of millivolts. Also note that during the pulse transmembrane potential changes from the resting potential of ~−86 mV to close to the threshold potential of ~−57 mV. Starting from this for construction have been chosen the pulse waveforms with segments altering the transmembrane potential at 10 mV (3 segments), 3 mV (10 segments) and 1 mV (29 segments). Selection was caused by a desire to assess the energy-effectiveness of pulses with different number of segments.

The threshold energy ratios of the three constructed waveforms were compared to that of the previously studied half-sine waveform which had been built using one segment of the sinusoidal function (sine) [

An example illustrating the impact of the 10-segment pulse on the cardiomyocyte model is given in

The energy-optimal pulse waveforms and that of the energy-optimal half-sine pulse obtained in the simulation process are shown in

It should be noted that the duration of the energy-optimal rectangular pulse in the threshold excitation energy pattern is 11 ms for a Luo-Rudy cardiomyocyte membrane [

The parameters of the energy-optimal pulse waveforms are shown in

Interestingly enough, all of the new energy-optimal pulse waveforms tend to share the same features-a shallow rise and fall, with the duration of the rise being about 1.5 times longer than that of the fall (asymmetric pulses). The half-sine pulse also has a shallow rise and fall, but their duration is the same. As can be seen from

Pulse | Threshold Current Density Amplitude in µA/cm^{2} | Threshold Energy Ratio in µA^{2}∙ms/cm^{4} | Relative Threshold Energy |
---|---|---|---|

3 segment | 5.93 | 241.7 | 1.00 |

10 segment | 5.69 | 240.8 | 1.00 |

29 segment | 5.66 | 240.9 | 1.00 |

Half-sine | 5.55 | 242.9 | 1.01 |

^{2}∙ms/cm^{4} (the relative threshold energy being 0.95) [

Noteworthy is the fact that during external defibrillation the threshold sloped pulse energy is decreased through reduced resistance of the chest, which was recorded during the pulse current surge [

The present and previous our papers have focused on monophasic and first phase biphasic pulses of different waveforms (morphology) and duration which releases at least 70% - 80% of the pulse energy on the heart region during defibrillation [

According to the results of the computer simulation, the Gurvich-Venin quasi-sinusoidal biphasic pulse (1972) proves to be close to the optimal as the previously studied first phase of which has a threshold energy factor equal to 249.2 μA^{2}∙ms/cm^{4} (relative threshold energy being 1.03) [^{2}∙ms/cm^{4} (relative energy threshold being 1.14) [

Does all of the above imply that there exists a possibility for a significant reduction of defibrillation pulse energy? There are objective prerequisites for this. During the experiments on animals [

Constructed energy-optimal monophasic defibrillation pulse waveforms do not substantially differ in their threshold energy ratio from an energy-optimal half-sine pulse. A characteristic feature of all the above pulses is their shallow rise and fall. The above data obtained using the Luo-Rudy cardiomyocyte membrane model suggest that it is not possible to significantly increase energy efficiency for classic monophasic and, most likely, biphasic defibrillation pulses. On the other hand, the data obtained in the experimental studies [

Vyacheslav A.Vostrikov,Boris B.Gorbunov,Sergey V.Selishchev,11, (2015) Construction of Energy-Optimal Smooth Monophasic Defibrillation Pulse Waveforms Using Cardiomyocyte Membrane Model. Journal of Biomedical Science and Engineering,08,625-631. doi: 10.4236/jbise.2015.89058