# Electronic Emulator of Biological Tissue
## 2 Methods and Materials
### Circuit Model
#### 2.2.2 Multiple Monopolar Pulse Model  
With a higher repetition frequencies, in our case 4717 Hz, it was observed that the current reaches around 75% of the final amplitude at the first pulse and percentage than exponentially rises with pulses, while all pulses in sequence have the same shape and amplitude in case of 1 Hz repetition frequency [19]. Already [PERSON] et al. showed that for pulse repetition frequencies above 1 kHz a significant change in pulse shape occurs, meaning the following pulses start at higher initial value [31]. Heat generation, diffusion of intracellular content and pore lifetime could explain these phenomena [31; 32; 33]. Therefore in parallel to inductor \(L_{1}\) an additional resistor \(R_{4}\) and diode in series are added (Scheme 2). A diode emulates an \"electroporation\" memory while resistor \(R_{4}\) emulates the loss of memory. For the first pulse in a pulse sequence with higher repetition frequency, the situation is the same as for first/single pulse or pulses with lower repetition frequency (Scheme 1). The electroporation memory is not yet present. During the pulse, the inductor \(L_{1}\) is magnetized and right after the pulse, during the pause between pulses, the \(L_{1}\) current in the model regarded as \(I_{M0}\) starts to flow through the new resistor \(R_{4}\) and the inductor is in a demagnetization phase until the next pulse arrival. \(I_{E}\) is still present when the next pulse is generated because the pause between the pulses is shorter than inductor demagnetizing time. Therefore the \(I_{E}\) increases, it is the sum of inductor magnetize current and \(I_{mem}\) memory current. The inductor current for second and all other pulses is calculated in according to (Equations (5) and (6)):  
\[I_{L}(t,N)=(\frac{U_{amp}-U_{th}}{R_{3}}-I_{mem}(N))\times(1-e^{-(t-(N-1) \times T_{per})/\tau_{2}})+I_{mem}(N) \tag{5}\]  
\[I_{mem}(N)=I_{M0}(N)\times e^{-T_{puse}/\tau_{3}} \tag{6}\]  
in which, \(N\) is a pulse number, \(I_{M0}\) represents a current at the end of the previous pulse, \(T_{puse}\) is equal to the duration of the pause between pulses and \(T_{per}\) in pulse period (\(T_{per}=T_{pulse}+T_{puse}\)). Figure 2: Flow chart of numerical calculations in Matlab. All the calculated optimal component values calculated in previous section (\(R_{1}\), \(R_{2}\), \(R_{3}\), \(C_{1}\), \(L_{1}\)) are the same also in case of multiple monopolar pulse model, only threshold voltage was optimized again and \(R_{4}\) which enables memory current was again defined by using LSE regression. In this case, the whole sequence, all eight pulses were, included in the calculation. Because only one variable \(R_{4}\), was left undefined, a range of potential \(R_{4}\) values was extended, meaning a lot higher number of potential values were included in the regression. Final circuit emulator (Scheme 3) is based on equations (Equations (7)-(10)), which are only valid for the time of the pulse (\((N-1)\times T_{per}<t<(N-1)\times T_{per}+T_{pulse}\)), and well describe the behaviour of our specific biological tissue. \[I(t,N)=\left\{ \begin{aligned} &\frac{U_{amp}}{R_{1}}+\frac{U_{amp}}{R_{2}} \times e^{-(t-(N-1)\times T_{per})/\tau_{1}},&\quad U<U_{th}\\ &\frac{U_{amp}}{R_{1}}+\frac{U_{amp}}{R_{2}}\times e^{-(t-(N-1) \times T_{per})/\tau_{1}}+(\frac{U_{amp}-U_{th}}{R_{3}}-I_{mem}(N))\\ &\times(1-e^{-(t-(N-1)\times T_{per})/\tau_{2}})+I_{mem}(N),& \quad U>U_{th}\end{aligned} \right. \tag{7}\]  
\[I_{mem}(N)=I_{M0}(N)\times e^{-T_{pulse}/\tau_{3}} \tag{8}\]  
\[I_{M0}(N)=\left\{ \begin{aligned} & I((N-1)\times T_{per}-T_{pulse}),& \quad N>1\\ & 0,&\quad N=1\end{aligned} \right. \tag{9}\]  
\[C_{1}=\frac{\tau_{1}}{R_{2}};\quad\quad\quad L_{1}=\tau_{2}\times R_{3}; \quad\quad\quad R_{4}=\frac{L_{1}}{\tau_{3}} \tag{10}\]  
Final load current for higher repetition frequencies is described with discrete equation (Equation (7)), where N is the pulse number, \(T_{per}\) period (pulse duration + pause).