# Electronic Emulator of Biological Tissue as an Electrical Load during Electroporation

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## Abstract

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## Featured Application

**Development of a analog electronic circuit that emulates biological tissue during high voltage pulse delivery and/or electroporation. A case study and a proof of concept with potential for development of an electroporator tester.**

## Abstract

## 1. Introduction

## 2. Methods and Materials

#### 2.1. Mathematical Model

#### 2.2. Circuit Model

#### 2.2.1. Single Monopolar Pulse Model

#### 2.2.2. Multiple Monopolar Pulse Model

#### 2.3. Electronic Load Emulator

## 3. Results

#### 3.1. Numerical Calculations

#### 3.2. PSpice Model and Electronic Emulator

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ECT | Electrochemotherapy |

PEF | Pulsed electric fields |

LSE | Least square error |

RMSE | Root mean square error |

## References

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**Figure 1.**(

**a**) Typical time course during PEF application to the tissue (red) and three mathematical functions (black); (

**b**) Current is modeled as a sum of a square wave pulse and two exponential functions, by following the equation (Equation (1)).

**Scheme 1.**Single monopolar pulse circuit emulator: equivalent circuit model of tissue during electroporation. Where ${V}_{ep}$ represent applied electroporation pulse, with pulse voltage amplitude ${U}_{amp}$ and ${U}_{th}$ electroporation threshold voltage.

**Scheme 2.**Additional in series connected resistor ${R}_{4}$ and diode in parallel to the inductor ${L}_{1}$, emulate an “electroporation” memory, which enables that the following pulse starts at the higher initial value.

**Scheme 3.**Final electronic emulator of biological tissue as an electrical load during electroporation.

**Figure 3.**Average of five current measurements of the first pulse at 1 Hz (yellow) and 4717 Hz (green) repetition frequency. (

**a**) Modeled current (red), optimal circuit parameter values were determined for each applied voltage separately for 4717 Hz pulse repetition rate; (

**b**) Modeled current (red), optimal circuit parameter values were determined with the LSE method, the cost function included all three currents at different voltages for pulse repetition rate 4717 Hz.

**Figure 4.**Average of five current measurements at 4717 Hz repetition frequency (green), (

**a**) numerically modeled current by Matlab (red, first row), (

**b**) modeled current by a PSpice (blue, second row) and (

**c**) measured current trough prototype emulator (purple, third row). An additional current measurement in the case of the emulator was added at the applied voltage set to 200 V, in order to present a current response, when the applied voltage is lower than the threshold voltage. In the first column, the current at 500 V in the second 750 V and third 1000 V applied voltage amplitude is presented.

**Figure 5.**A physical prototype electronic emulator of biological tissue as an electrical load during electroporation.

**Scheme 4.**Proposed emulator upgrade for electroporation with both polarity pulses, but additional current measurements should be analyzed in detail, to determine the relation between both inductors (${L}_{1},{L}_{2}$).

Voltage [V] | ${\mathit{R}}_{1}[\Omega ]$ | ${\mathit{R}}_{2}[\mathbf{k}\Omega ]$ | ${\mathit{R}}_{3}[\mathbf{k}\Omega ]$ | ${\mathit{C}}_{1}$ [nF] | ${\mathit{L}}_{1}$ [mH] | ${\mathit{U}}_{\mathit{th}}$ [V] |
---|---|---|---|---|---|---|

500 | 787.5 | 1.152 | 0.176 | 1.1 | 609,400 | 200 |

750 | 621.1 | 1.626 | 3.192 | 0.77 | 182.5 | 200 |

1000 | 639.9 | 1.401 | 2.393 | 0.65 | 106.9 | 200 |

**Table 2.**Optimal values of electronic components for the single positive monopolar pulse model are presented in the first line and for multiple monopolar pulse model in the second.

${\mathit{R}}_{1}[\Omega ]$ | ${\mathit{R}}_{2}[\mathbf{k}\Omega ]$ | ${\mathit{R}}_{3}[\mathbf{k}\Omega ]$ | ${\mathit{R}}_{4}[\Omega ]$ | ${\mathit{C}}_{1}$ [nF] | ${\mathit{L}}_{1}$ [mH] | ${\mathit{U}}_{\mathit{th}}$ [V] |
---|---|---|---|---|---|---|

682.4 | 1.287 | 1.287 | - | 0.998 | 57.5 | 400 |

682.4 | 1.287 | 1.287 | 171.1 | 0.998 | 57.5 | 366.7 |

**Table 3.**Final component value table, of components which were used in the PSpice simulation and prototype emulator.

${\mathit{R}}_{1}[\Omega ]$ | ${\mathit{R}}_{2}[\mathbf{k}\Omega ]$ | ${\mathit{R}}_{3}[\mathbf{k}\Omega ]$ | ${\mathit{R}}_{4}[\Omega ]$ | ${\mathit{C}}_{1}$ [nF] | ${\mathit{L}}_{1}$ [mH] | ${\mathit{U}}_{\mathit{th}}$ [V] |
---|---|---|---|---|---|---|

680 | 1.2 | 1.2 | 175 | 1 | 57.5 | 360 |

**Table 4.**The performance summary table displays the root mean square error between measurements on beef liver and mathematical model ($RMS{E}_{M}$), or prototype emulator ($RMS{E}_{E}$) or resistor ($RMS{E}_{R}$) and mean standard deviation of five measurements on beef liver (${\sigma}_{liver}$).

SET VOLTAGE, REP. F | ${\mathit{\sigma}}_{\mathit{liver}}$ | ${\mathit{RMSE}}_{\mathit{M}}$ | ${\mathit{RMSE}}_{\mathit{E}}$ | ${\mathit{RMSE}}_{\mathit{R}}$ |
---|---|---|---|---|

[mA] | [mA] | [mA] | [mA] | |

500 V, 1 Hz | 38.5 | 40.3 | 38 | 101.1 |

500 V, 4717 Hz | 46.3 | 125.8 | 132.1 | 101.4 |

750 V, 1 Hz | 115.1 | 111.6 | 106.2 | 72.6 |

750 V, 4717 Hz | 124.7 | 41.4 | 40.7 | 471.4 |

1000 V, 1 Hz | 116.1 | 192.7 | 189.5 | 131.6 |

1000 V, 4714 Hz | 177 | 55.7 | 58.1 | 705.7 |

Total RMSE | 108.87 | 356.7 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Pirc, E.; Balosetti, B.; Miklavčič, D.; Reberšek, M.
Electronic Emulator of Biological Tissue as an Electrical Load during Electroporation. *Appl. Sci.* **2020**, *10*, 3103.
https://doi.org/10.3390/app10093103

**AMA Style**

Pirc E, Balosetti B, Miklavčič D, Reberšek M.
Electronic Emulator of Biological Tissue as an Electrical Load during Electroporation. *Applied Sciences*. 2020; 10(9):3103.
https://doi.org/10.3390/app10093103

**Chicago/Turabian Style**

Pirc, Eva, Bertrand Balosetti, Damijan Miklavčič, and Matej Reberšek.
2020. "Electronic Emulator of Biological Tissue as an Electrical Load during Electroporation" *Applied Sciences* 10, no. 9: 3103.
https://doi.org/10.3390/app10093103