**4. Bulk electroporation**

for single cell electroporation, electric field is in inhomogeneous form, which targets on a particular cell without effecting neighboring cells. Generally cell membrane described in terms of fluid mosaic membrane model [64]. Due to application of an electric electric field, the formation of pores into the cell membrane depends upon field strength with low conductance, which is approximated as electrical capacitors with infinite resistance. The pore as liquid capacitor which converts to the electrical force associated with transmembrane potential U into an expanding pressure within the aqueous pore interior [65-68]. The pore creation energy ΔE can be calculated with pressure balance by removal of planar area πr<sup>2</sup> and creation of a

> <sup>2</sup> D = P -P G *E rr* 2 g

2 4 D = P -P G+ *Er r r A r* () 2 g

where surface energy approximately Г= 1× 10 J/m<sup>2</sup> and the edge energy approximately Υ= 1 to 6 × 10-11 J/m [69-71]. Here Υ is constant even it is a function of r [70, 72-73]. To expand the pore

The first term is energy related stressed pore edge with length 2πr. The second term is energy to remove a circular flat lipid membrane having energy per unit area Г and the third term is steric repulsion of the lipids with constant A. Fourth term arises when transmembrane

The transmembrane potential ΔΨE, in a uniform electric field E at a point M with time t can be

 q

where f is the shape of the spheroidal cell [74] and τ is the charging time of the cell membrane, g depends upon the conductivities and R is the radius of the spherical cell. E is the field strength and θ(M) is the angle between normal to the membrane at the position M and direction of the field [55]. The exponential term can be ignored if the pulse length is longer than a few microseconds. Because induction time τ<1µs, the value f is generally 3/2, which is for com‐

( ) ( ) cos ( ) (1 exp( / )) *E in out* D = - =-

*t fg RE M* ´- -*t*

 l (5)

/ (6)

2 2 0.5*CV r p m* - (7)

t

(8)

cylindrical pore edge of length 2πr, can be written as

72 Advances in Micro/Nano Electromechanical Systems and Fabrication Technologies

radius from zero radious to r can be written as

potential Vm is nonzero, which is related to,

y

pletely insulating membrane [75].

 yy

written as

### **4.1. Electric field effect on cell membrane**

Biological systems are mainly heterogeneous from electrical point of view [76-77]. When a high electric field pulses is applied across the cell membrane, due to rapid polarization, cell membrane can deform mechanically (e.g., suspended vesicles and cells) and is allowed to redis tribute ionic charges due to electrolyte conductivities and distributed capacitance. Initially every bilayer cell membrane structure is dielectric in nature. After application of electric field pulses, membrane conductivity can increase due to structural change of the cell membrane cause the formation of hydrophilic pores from initially formatted hydrophobic pores [78]. Generally the breakdown potential of lipid bilayer is 100-300 mv, which depends upon the lipid compositions [79]. If the pulse electric field (PEF) decreases, then breakdown voltage can increase [80-81].

To consider a cell as a sphere with a small volume of V and current is flow of charges. Both current and charges have relationship between them. If we consider the total current flow through small volume of cell V, then the current must be equal to the net flow of charges with in volume V or equal to the rate of decrease of charge with in volume or net flow of current into volume V must be accompanied by an increase of charge with in volume V. This is the principle of conservation of charge, which can be mathematically expressed as

$$I = \int\_{S} J \, ds \tag{9}$$

$$=-\frac{\partial}{\partial t}\int\_{V}\rho dV\tag{10}$$

Using divergence theorem, *∫ S A*.*nds* =*∫ V* ∇.*AdV* then the equation can be written as

$$\int\_{V} \nabla \cdot \mathbf{J}dV = -\int\_{V} \frac{\partial \rho}{\partial t}dV\tag{11}$$

where J is the current density and ρ is the volume charge density. Now we can write equation [11] as

$$\int\_{V} \left(\nabla J + \frac{\partial \rho}{\partial t}\right) dV = 0 \tag{12}$$

Since equation [12] must be true irrespective of the volume, so we can write equation [12] as

$$
\nabla \cdot f + \frac{\partial \rho}{\partial t} = 0 \tag{13}
$$

This is equation of continuity, which is the principle of conservation of charge where steady current involve ∂*<sup>ρ</sup>* <sup>∂</sup>*<sup>t</sup>* =0 and if charges are not generated into the cell during application of electric field pulses, then ∇.*J* =0. Now electric field is the gradient of electric potential. So Maxwell equation becomes *Δ* <sup>2</sup> *ψ*=0, where Ψ denotes the electrical potential. If the conduc‐ tivity of cytoplasm and external medium of the cell is higher than the cell membrane conduc‐ tivity, then ΔΨ, the field induced transmembrane potential can be written as:

$$
\Delta\psi = 1.5 a\_{\text{cell}} E\_e \cos\theta \tag{14}
$$

where acell is the outer radius of the cell, Ee is the applied electric field strength and θ is angle between field line and normal to the point of interest in the membrane which can be either 00 or 1800 [82-85]. Under the ideal experimental conditions like pulse width, electric field, number of pulses, removal of external electric field for resealing of the pore membrane, pulse duration and rearrangement of the membrane protein can be preserved the cell viability. If the membrane is not spherical, then equation [14] may not be right explanation. If we consider that the cell has ellipsoidal structure, then equation [14] will not be applicable. But for any practical purpose this equation can be used to evaluate the field induced transmembrane potential.

### **4.2. Reversible electroporation**

When a strong external electric field applied across cell and tissue, then membrane conduc‐ tance and permeability can increase significantly due to strong polarization of the cell mem‐ brane, as a result membrane can form nano scale defects (called nanopores). But when we switched off the external electric field, membrane can return from its conducting state to its normal state. This phenomenon is called reversible electric breakdown or reversible electro‐ poration [86-87]. The reversible electroporation generally involves reversible electric break‐ down (REB), which is generally a temporary high conducting state. This reversible electroporation influences both cell membrane as well as artificial planner bilayer lipid membrane. Reversible electroporation involve with rapid creation of many small pores, where membrane discharge occur before any critical pores can evolve from the small pores. To understand the method of electroporation of bilayer lipid membrane, it is necessary to use the method of voltage clamp [65,71,88] and charge relaxation [80,89] techniques, where for charge relaxation, kinetics of voltage decreases across the membrane after the application of short pulses (20 nsec to 10 µsec). It was also fact that originally membrane breakdown can occur before the start of membrane discharge. From the charge relaxation method, it used to show that, when membrane of oxidized cholesterol are rapidly (~ 500nsec) charged ( approximately 1 V), then membrane resistance reversibly decreased by almost nine orders of magnitude [80, 89]. By this way it was first observed that reversible breakdown of planner lipid bilayer membrane and the charged could not be exceeded beyond 1.2 V, even pulse amplitude was increased further. After first electroporation, it was able to recharge again. This same phe‐ nomenon was investigated later with azolectin bilayers modified UO2 2+ ions and the mem‐ branes of lecithin and cholesterol in the presence of alkaloid holoturin A [90-92]. The different types of behavior of planer oxidized chelosterol membrane are shown in table III [78,80,93].


**Table 3.** Planner bilayer membrane electroporation. Permission to reprint obtained from Elsevier [78, 80, 93].

For voltage clam method, the time resolution is 5-10 µs to monitor continuously charge at specific conductance of membrane from 10-8 to 10-1 Ω-1/cm-2. Thus voltage clam technique and charge relaxation technique are complement to each other [94].
