Reversible electroporation study of realistic normal and cancerous cervical cells model using avalanche transistor based nanopulse generator

In this paper, we study the reversible electroporation process on the normal and cancerous cervical cell.The 2D contour of the cervical cells is extracted using image processing techniques from the Pap smear image. The conductivity change in the cancer cell model has been used to differentiate the effects of the high-frequency electric ﬁeld on normal and cancerous cells. The cells modulate themselves when this high-frequency pulse is applied based on the Debye relaxation relation. In order to computationally visualize the effects of the electroporation on the cell membrane Smoluchowski equation calculates the number of pores generated and Maxwell equations are used to determine the Transmembrane potential generated on the membrane of the cervical cell. The results produced demonstrates that this mathematical model perfectly describes the numerical tool to study the normal cells and cancerous cells under the electric ﬁeld. The electric ﬁeld is provided with the help of a realistic pulse generator which is designed on the principle of Marx circuit and avalanche transistor-based operations to produce a Gaussian pulse. The paper here use strength duration curve to differentiate the electric ﬁeld and time in nanoseconds required to electroporate normal and cancerous cells.


Introduction
The cervical cancer is the most common occurrence in women as per data given 1 . The conventional Pap smear test or liquid cytology-based test is performed which is expensive and the false rate is high around 40 . Various methods have been proposed to detect cervical cancer 2 . The reversible electroporation method can be adopted as it can easily be used for drug delivery and dyes can be easily transported to the cytoplasmic area by the formation of pores in the cell membrane if a sufficient electric field is applied for nanosecond time as it generates a transmembrane potential that is around 1V to 1.5 V 3-8 . The mathematical model has been proposed for the study of pore formation and the amount of trans-membrane potential generated during electroporation 7 . The microdosimetry study has been used to generate models that are reliable for quantitative analysis of pores and the transmembrane potential induced in the cells 9 . Thus, these models can give a clear indication as to how much amplitude, waveform, and frequency content must be applied to design and optimize the pulse generator for electroporation studies 9 . The human neuroblastoma cells geometric model has been extracted for microdosimetry work in earlier literature 10 . The image processing techniques have also been used to accurately extract the contour of the cells in 2D 10 . Another work has been published to accomplish this task by using the parametric curve such as the Supergielis formula to generate the geometry that nears the irregular cell 7 of the Jukart cells. This formula has also been used in numerous literature for replicating muscle cells as well as Red blood cells 11 . Efforts have also been made to generate 3D models of the cell 12 . In the case of cervical cells, rectangular parallelopiped geometry has been proposed to carry out the FEM based numerical analysis and was able to give accurate dimensions of the various types of normal cervical cells and their respective stages of cancer cells dimension variations in cytoplasmic as well as in the nucleus region 13,14 . The cervical cancer tissue has been studied for irreversible electroporation process where the conductivity change is represented using the asymmetrical sigmoid Gompertz curve function and experimentally verified. The changes in the conductivity by a factor of 1.8 has been observed 15 . This change in the conductivity of tumor cells in the solution has been also observed using electric conductivity measure using 3T MRI techniques 16 . Most of the literature have demonstrated a change in the conductivity of cancerous cells and the disruption of the cell membrane in cancer cells as a result of electronegativity thus resulting in a reduction of membrane potential 17 . A high concentration of Na and Cl is found in the cancer cells 19 . The efficiency of the given numerical model depends on the morphology of the cell introduced in the electroporation area and the electric field pulse also provided 5 . The dispersive and nondispersive models are provided to study the effects of electroporation in the earlier studies 5 but the dispersive model has been found out to have low permittivity at large frequencies hence, more Transmembrane voltage. The comparison between the both has been provided by many earlier works 5,7 and it has also been found that a low amount of electric field is required by the dispersive model to generate the transmembrane potential. Another major problem is found in the computation as the membrane layer is found to be around 5 nm 5, 7 thus the concept of the thin layer is used to lower the computational requirement.

Extraction of geometry from cervical cell image
In this method, we use K-clustering and image processing techniques to extract the 2D geometry of the cervical cells mainly superficial and intermediate single pap cells from the image data set as shown in Figure 1. The two-dimensional cells are then converted to three-dimensional cells for further analysis.

Image acquisition
The images of the cervical cells are available on the website of MDE-lab, University of the Aegean 18 . The data set consists of 917 single pap cells. The cells of normal and intermediate cervical cells were taken from the data set for the extraction of contour using image processing techniques. The data set consists of around 74 normal superficial cells and 70 normal intermediate cells.
In this paper, we have randomly selected a few to demonstrate the contour extraction procedure.

Image denoising
The presence of noise in the image is the major challenge in the field of image processing. The pap smear images consist of noise hence the quality of the picture is reduced. The denoising method called nonlocal means to suppress the noise in the images. The python 3.7 software was used for processing the image using the Open source computer vision (OpenCV) library. The library has already built-in functions for filtering using a nonlinear filter for denoising colored images. This method removes Gaussian noise from the image due to which the cytoplasmic area in the image gets cleared as the image it is observed having particles resembling Gaussian noise. Thus an image with a well-defined boundary and nucleus can be observed.

K-means clustering algorithm for cell segmentation
The K-means clustering perfectly segments the nucleus and the cytoplasmic area from the pap images. The image was segmented into three groups nucleus, cytoplasm, and background using the k-means algorithm. The histogram analysis of the image is done which gives the intensities. The k-clusters centroids were initialized with three centers. Each intensity distance was calculated and shortest distance intensities were clubbed together from the centroids initialized. Then new centers are assigned by calculating the mean of all the members in their respective clusters. Thus repeating the last steps till no change in the image is done.

Morphological operations for contour detection
Now the segmented image is binarized 20 . We use MATLAB 2020b for this operation and use the inbuilt function of drawing perimeter and getting the contour of the image. We get the respective contours of the image in two-dimensional space. The image is then a vector image, QCAD an open-source is further used for modification of the image. The cervical cell's dimensions are changed by the transformation method and reshaped according to the dimensions of the cell 13,14 . The Table 1 below shows the dimensions of the cell.

Geometry model of cervical cell
The cell model used in earlier studies has regular geometry like a circle or ellipse sometimes a combination of both the geometries. They gave an inaccurate result as they were not close to the representation of the realistic cell geometry. A new method of using the Supergielis formula has been put forward which creates an irregular cell geometry.
Where m 1 =m 2 =3, b 1 =30, n 1 =n 2 =15, θ ∈[−π/2, π/2] are the parameters to create the required to create the geometry of superficial cervical cells. The parameters k x and k y are the scaling factors with a 1 and a 2 being the positive real numbers.The output of this parametric curve is shown in the Figure 4.

Avalanche transistor
Avalanche transistor is used for high-speed pulse operation. They have high frequency and low impedance.There are many ordinary transistors available for avalanche operation such as 2N2222,2N5551,2N2396a,2N23907 available for avalanche operation 21 . Zetex has provided for a range of FMMT series avalanche transistors for high voltage operations such as FMMT411,

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FMMT413, FMMT415, and FMMT417. These operate in a very high voltage operation region as the breakdown voltage of these circuits lies in the range of 80 V to 320 V. These have inbuilt Zener diodes, switches, and inductors for avalanche operation. Together with the Gummel-Poon model they give the respective output in simulation 22 . Hence, it is easy to simulate these circuits as the manufacturers provide the spice model and diode connections but ordinary transistor does not have such components hence the avalanche operation simulation is difficult as the transistors are based on simple Gummel-Poon model. Hence, additional current sources were added to demonstrate the operation 23 . This model perfectly depicted the avalanche operation in the generators. A spice sub-circuit script is written to add the multiplication factor based on avalanche theory. The supply voltage has been considered between the range of 60 V to 100 V DC due to the limited operating range of the transistor. The 2N2396a transistors are cheaper easily available and quite frequently used for many transistor applications. There are many avalanche transistors available the selection basis must be the supply voltage available such that the avalanche breakdown occurs. The breakdown is represented by a simple equation I C1 = MI C1 where M is the multiplication factor represented by equation Where U br represents the breakdown voltage and N is a constant depends on the BC junction type and material used. Generally, the value of N varies between 4 and 6 23 .

Marx generator
The simulation of the Marx generator is performed in MATLAB Simulink 2020b. In order to perform the transistor 2N2396a spice, a sub-circuit is imported which has been added with current sources as explained earlier. The resistance of R C1−5 =R C 1−4 =4.7 kΩ and C 1 to C 5 = 1nF Figure 2. a) shows the basic operation of the five-stage Marx generator 2425 . The voltage provided by the DC source is less than V cbo which is 60V. The simulation output of the Marx generator is shown in Figure 2.c) and the output of the digital oscilloscope TDS210 is shown in Figure 2.d) and the terminals are reversed for taking positive output. The output has been reduced using a voltage divider arrangement to get the required output. The load is taken R L =50Ω. The input trigger is provided using a monostable multivibrator with 555 timer IC and RC differentiator circuit to the transistor T 1 .The hardware prototype is shown in Figure 2.b). The five-stage Marx generator is given by the formula Where R L is the load and N is the number of stages of marx generator.The r represents the internal resistance of the avalanche transistor.

Modeling of cervical cell permittivity model
The Multi-relaxation Debye-based relationship is used to model the cervical cell dielectric properties. The cytoplasm and nucleus of the cervical cells in this study uses a dispersive medium whose dielectric properties has been modeled using a second-order equation 5 .
ε ∞ denotes the high frequency permittivity,with τ 1 and τ 2 are the relaxation time and ∆ε 1 ,∆ε 2 are the relaxation amplitude. The polarization vector P can be expressed in the second-order differential equation which is known as Debye Dispersion model.In this equation, the polarization P is expressed as a time-varying model of a homogeneous medium in terms of a time-varying electric field given by:

Pores formation model of cervical cell
The application of the nano pulse electric field causes pores on the membrane layer which is made up of a bi-lipid layer. The pores generated are assumed to have a radius of r p =0.8nm. The dynamics of the creation of pores and resealing is solved by using an asymptotic Smoluchowski's equation: where N denotes the pore density on the plasma membrane,α and q denotes the electroporation parameters,V ep is the characteristic voltage of electroporation, and N 0 represents the initial pore density. The electroporation increases the conductivity of the membrane at each time and as the transmembrane potential changes at every step in time the no of pores is updated and the conductivity is different positions in the cell membrane. The average conductivity of the cervical cell membrane at different regions where pores are formed is given by the equation, σ (x, y,t) = σ 0 + πσ p r p N(x, y,t)K where The energy barrier inside the pore is given by w 0 in equation no. and η is the relative entrance length of the pore and the non dimensional transmembrane voltage is expressed as υ m = q e KT v m .

Electromagnetic modelling of the cervical cell
The electric pulse from the device is applied to the upper and lower copper plates of the simulation model.The electric potential is calculated by solving the Laplace equation :

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The equation in conjunction with equations 10,12,13 are used along with equation The Transmembrane potential (TMV) is calculated using a special boundary condition present in COMSOL 5,5 on the cell membrane to reduce computational need which is distributed impedance present in the electric current module of the multi-physics operations. This Distributed impedance boundary layer is used in the parametric curve model and 2D realistic model as the membrane layer is very thin around 5 nm represented by equation 16.

Discussion
The method proposed is compared with the actual cervical cell and cancer cervical cell electroporation provided by the literature of irreversible electroporation of cancerous cervical cell 15 . The method uses an actual pulse generated from the avalanche transistor-based pulse generator simulation results rather than an inbuilt function to generate a Gaussian pulse for study. The simulation study using Gaussian pulse has the advantage of reduced artifacts due to the smooth rise and fall time of the pulse. The whole Transmembrane voltage was taken at an angle θ =90 where the electric field is directly exposed on the top of the cell membrane. The pores formation when is about 10 14 and above the cells are found to be electroporated. The Figure 4 represents the contour of superficial cell generated by the use of parametric curve and can be easily observed that the TMV and pore density formation validates that the pulse generated can easily electroporate the cells.
The electroporation relative length(EPRL) of the the realistic cell contour and the parametric curve generated shows a great difference.The EPRL is represented by formula EPRL(%)= (length of the electroprated region)÷(Total perimeter of the plasma memberane)× 100 The EPRL of the parametric curve was found to be 37.2 %. Thus the cell morphology plays an important role in the formation of pores and transmembrane generation. A simple parametric curve cannot get the minute changes in morphology that the cells brought from the image processing application can bring out. The orientation of the cervical cells with respect  to the electric field has also a considerable effect on the EPRL. The more the cell length directly exposed to the electric field larger is the EPRL for the cells. The Table 2 Shows all the EPRL generated of the cells given in the order Figure 1 where the EPRL is the area in which the pore density is in order 10 14 or above. The cancer cell model is also extracted with help of image processing which is the first stage of cancer cell also known as the Cervical intraepithelial neoplasia (CIN1) stage of intermediate cell Figure 6 (a). The conductivity of cancer cells rises by a factor of 1.8 as stated in the literature survey 15 .This the maximum increment in the cervical cancer cell. The method proposed is to study the effect on the pore density due to a change in the conductivity of the cell. The Figure 6 (c) shows that as there is an increase in conductivity of the cell due to the cancer formation pore density increases when an electric field is applied . A concept of the Strength duration curve of the cells to plot and observe the threshold electric field and time required for pore formation is introduced in the literature 29 . The analysis in a similar way is done for normal and cancer cells by changing the conductivity by factor multiplication in steps (1.2, 1.5, 1.8). The results are then analyzed by plotting them in the graph as shown in Figure 7. It can be easily observed that the cancer cells require less amount of threshold electric field and duration as compared to the normal cells to electroporate.

Conclusion
In this paper, the two-dimensional contour extraction of cervical cell images was performed using image processing techniques. The Marx pulse generator was built using avalanche transistor was used to generate a Gaussian pulse of nanoseconds duration. The hardware and simulation analysis has been done to demonstrate the working of the generator. The contour and the pulse generated were taken into the multiphysics area for a more realistic study of reversible electroporation. The dispersive cell medium and Smoluchowiski equation were used to generate the required Transmembrane potential produced on the cell membrane. The SuperGielis model was also implemented to reproduce the cervical cell model. The electroporation relative length (EPRL) was calculated to show the difference in the area of electroporation in the case of the parametric curve and the extracted contour. This model also used the dispersive medium to show the variation in the effects of reversible electroporation. This work was also used to extracted the morphology of the cervical cancer cell. The change in the conductivity of the cell due to the tumor formation was used to find the threshold electric field required to give reversible electroporation to the cell. The strength-duration plot is provided to demonstrate the difference in the electric field needed to electroporate the normal and the cancerous cervical cell. Thus, after a detailed analysis it was found that the cancer cells require less electric field and time to electroporate than the normal cells due to the conductivity increment as a result of a high content of sodium chloride in the cancer cell. Thus, the paper validates the hardware, addition of image processing techniques for microdosimetry analysis, change of conductivity in cancer cells and its effect on pore density when the electric field is applied and the threshold electric field of both normal and cancer cells. In future, multi-cellular cervical cells with both normal and cancer cells can be extracted and analyzed to get the idea of the electric field needed for electroporation of the cervical cells.