  electroporation , a nonthermal phenomenon , is used to enhance the permeability of biological cells and tissues [ 14 ] . here , an attempt has been made to study the electric field 's effect on tumor tissues thereby leading to the efficacy of electroporation .
electroporation involves the rapid structural rearrangement of membrane , in response to an electrically applied electric field .
a noticeable effect is a rapid increase in electrical conductivity attributed to the formation of pores in the bilayer lipid membrane .
literatures have shown significant trend of progressive electrical changes according to the proliferative characteristics of breast epithelial cells .
physiologists also further postulated that malignant transformation resulted from sustained depolarization and a failure of the cell to repolarize after cell division , making the area where cancer develops relatively depolarized when compared to their nondividing or resting counterparts .
it leads to the rupturing of membrane wall which can be either reversible or irreversible .
electroporation generally depend upon the magnitude and the duration of the voltage , and the field applied .
the membrane potential vm is given as  
 ( 1)vm=1.5ercos , 
					 where r is the cell radius and  is the angle between the electric field e and the radius vector .
a detailed study of electric field distribution is necessary for an effective understanding of the tissue 's behavior when subjected to electric field . in this study
the behavior of tissue and the effect of electric field on them are noted in each case .
literature has indicated that changes in the electrical properties of abnormal breast are more significant compared to the breast normal tissues .
the surface potentials are sensitive to the presence of tumour , location and placement of the electrodes .
the results can be used as a complement to experimental analysis , essential for effective manipulation of tissues for practical , real - life applications , such as electroporation - mediated gene therapy and enhancement of chemo - drug delivery ( electrochemotherapy ) [ 14 ] .
for fast and accurate simulation results , we chose the maxwell 's fem software from ansoft corporation , usa . for this simulation study , a slightly modified version of the more detailed electrical model of a tumor tissue reported by surowiec et al .  
three - dimensional models of breast lobe with single tumor and normal cell , with two tumor cells and two normal cells , are simulated for both needle and plate electrode configurations .
the maxwell simulator is an interactive package that uses finite element analysis ( fea ) to solve three - dimensional electrostatic problems .
the normal and the tumor cell permittivity and conductivity parameters used for the model are shown in table 1 [ 9 , 10 ] .
a high voltage of the order of 1200  v / cm is applied at 1  khz frequency .
the electric field across the tissue model for plate electrodes configuration is shown in figures 2 and 3 for normal and tumor cell tissues .
the electric field intensity is more for the normal cell tissue than the tumor cell tissue .
this could be due to change in membrane structure , composition , and minerals in the tumor cell compared to the normal cell .
similar results were obtained also for needle electrode configuration ( figure 4 ) . from this electric field
distribution values , the transmembrane potential is calculated for the applied voltage . also , from the 3d simulated model of different tissue model the capacitance value is noted and this value is applied to the electrical model using matlab . for this simulation study ,
a slightly modified version of the more detailed electrical model of a cell reported by schoenbach 's team [ 12 , 13 ] is used .  
the entire breast lobe with tissues is assumed as a single cell , and simulation is done . here
, the tissue is modeled as a homogenous conductive medium ( cytoplasm ) surrounded by a leaky dielectric membrane . in the above electrical model ,
the capacitance of the normal cell is replaced by the capacitance value obtained from the ansoft model of the cancer cell developed in this study . to this electrical model , a pulsed electric field of the order of 1200 
v / cm is applied with a pulse width of 100  sec and for a time period of one second . the variation in voltage ( y - axis ) across each element with respect to time ( x - axis )
is shown in figures 610 for various tissue models studied using plate electrode configuration .  
figure 6 shows the voltage across various cell elements , such as nucleus , plasma , and conductive cytoplasm for tissue with a normal cell and a tumor cell . 

figure 7 shows the voltages for a tissue with two normal cells and figure 8 shows that of a tissue with two tumor cells ( plate electrodes ) .
there is noticeable difference between the voltages and their profiles for various elements between these two electrode configurations indicating the effect of electrode on the electroporation efficacy [ 14 , 15 ] . 

figure 10 shows the influence of the electric field orientation on the transmembrane potential ( tmp ) .
the orientation is varied from 0 to 70 degrees , and the tmp is evaluated for the applied voltage between the electrodes . it can be inferred that the transmembrane potential tends to decrease with increase in orientation . also , the transmembrane potential of tumor tissue is less than that of the normal tissue .
this could also be attributed to the altered cell membrane and other cell parameters of the tumor cell compared to the normal cell . 

table 2 shows the influence of the electric field orientation on the nuclear membrane potential ( nmp ) .
the orientation is varied from 0 to 70 degrees , and the nmp is evaluated for the applied voltage between the electrodes .
also , the nmp of tumor tissue is less than that of the normal tissue .
this could also be attributed to the altered cell membrane and other cell parameters of the tumor cell compared to the normal cell .
a healthy cell membrane potential is strongly linked to the control of cell membrane transport and proliferation mechanisms as well as dna activity , protein synthesis , and aerobic energy production . since cancer cells can not maintain a normal membrane potential , they will have electronic dysfunctions that will impede repair and the reestablishment of normal metabolic functions . therefore
, a key therapeutic method for cell repair and cancer treatment would be to reestablish a healthy membrane potential in the body 's cells .   in our research
, the electric field distribution in normal and tumor tissues was investigated using 3d finite element analysis for plane and needle electrode configurations .
the tumor tissues shows lower intensities of electric field compared to the normal tissues , possibly due to the altered characteristics of membrane potential , its composition and minerals such as potassium , magnesium , sodium , and calcium .
these results demonstrate the susceptibility of malignant cells to the electric field application and the relative robustness of the normal cells , illustrating the enhanced efficacy of the electrochemotherapy using lower drug doses .
the field analysis results can be used for assessing effective treatment parameters of tumor tissues .   
the electrical characteristics of the membrane and the cytoplasm , such as the conductivity and permittivity of the membrane and the cytoplasm , as well as membrane thickness also govern the response due to electroporation in addition to the intensity and distribution of the electric field applied .
our results indicate that electric field analyses could be used for selecting suitable parameters for effective treatment of tumor tissues , since these parameters need to be optimized for various tumors / tissues and cells .
 an attractive alternative treatment for malignant tumors that are refractive to conventional therapies , such as surgery , radiation , and chemotherapy , is electrical - pulse - mediated drug delivery . 
 electric field distribution of tissue / tumor is important for effective treatment of tissues 
 . this paper deals with the electric field distribution study of a tissue model using maxwell 3d simulator . 
 our results indicate that tumor tissue had lower electric field strength compared to normal cells , which makes them susceptible to electrical - pulse - mediated drug delivery 
 . this difference could be due to the altered properties of tumor cells compared to normal cells , and our results corroborate this . 
1. Introduction
2. Simulation of Tissue Model
3. Results and Analysis
4. Discussion and Conclusions