Investigation of heat effects in pulse electric field treatment of cellular materials

Abstract

The paper deals with modeling and analysis of coupled electro-thermal processes during the pulsed electric field treatment of cellular materials for extraction of bioactive compounds. Subject of consideration is evaluation of heat effects: appearance of local thermal spots and high temperature gradients in the treated tissue. The presence of these phenomena is important for the processing: it aids the process of electroporation and thereby is useful for the extraction, but also could cause overheating and deterioration of the product quality. The analysis is provided using the finite element method, applied to the coupled time-dependent electric and transient thermal field problem. The mechanisms of heat transfer are studied by numerical simulations corresponding to the parameters (type and duration of electric pulses) of experimental examination of the processes of extraction of substances from vegetable seeds. Two steps are considered in the modeling: before and after electroporation. The field analysis after electroporation is carried out for correspondingly changed size and properties of the contact area between the cells. The obtained results can be used for adjustment of the process parameters in order to improve the yield of the extracted substances, without risk of overheating and degrading the quality of extracted product.

Keywords

Coupled electro-thermal field modelling cellular materials finite element method heat effects electroporation pulse electric field substances extraction

1. Introduction

In the recent years, great interest has been noticed in the electric field processing of biological materials, in relation with the potential applications and conditions for which field effects are expected [1–7]. The good knowledge and understanding of the mechanisms of interaction between electromagnetic fields and complex biological systems is essential for various applications: medical imaging, therapeutic treatment, physiotherapy and chemotherapy, food industry, etc.

The pulsed electric field (PEF) processing is a promising technology with variety potential applications in the bio-based and food industry [8–10]. The application of pulsed electric fields for disruption of cells in the processes of extraction of specific substances from plant cellular materials [11–21] is considered as alternative green technology with a lot of advantages [22] over the traditional methods: reduced processing time, reduced concentration of solvent, reduced energy consumption and improved extraction yield.

The principle of PEF treatment of biological cells or tissues is based on the applying of repeated short (microsecond range) high-voltage pulses that act on the cell membrane, causing an increase in permeability and/or a loss of integrity in the cell membrane [23–25]. It results in local structural changes electroporation) due to the formation of hydrophilic pores in the lipid bilayer because of very high local electric field gradients [20,26–29]. The rupture of the lipid bilayer is based on number [30] of complex related phenomena: electro-thermal [31–34] effect related to the increasing of transmembrane potential and the gradient across the cell membrane; electromechanical compression of the cell membrane [35–38]; physicochemical mechanisms [39,40] that lead to a reorganization/rearrangement of the lipid bilayer, and the combined effects between them. It has to be noted that the short-time processing enables reducing of the total energy consumption at temperature range well below the one associated with membrane phase transformation.

The great importance and wide applicability [8,9,22–24] of the method is a reason for many theoretical [36,37,41–43] and experimental [11,29,37,44,45] studies. The main factors [10,15,29,35,36,46] that influence the processes during the PEF treatment are the amplitude, duration and number of the pulses applied. The properties of the added solvent are also important for the extraction of substances from plant materials [45,47]. Appropriate determination of the PEF treatment parameters allows good quality and specific selection [12,13,19,47] of the extracted substances and their properties.

Despite the great number of studies, the coupled processes and multiphysics interactions taking part during the treatment of biological cells with pulsed electric field are not yet completely understood neither explicitly formalized [37]. The theoretical studies are mostly focused on the influence of the electric field on single cell and thus do not take into account the changes in the treated tissue due to interactions between neighboring cells. Although PEF processing is considered to be non thermal since the structure changes occur at significantly low energy levels, side thermal effects take place during the treatment. Because of the pores in the cell membrane and the subsequent exchange of intra and extracellular substances, as well the increase in the membrane conductivity, currents are flowing through the created conductive channels, causing a risk of overheating and hotspots [31,32]. Since the temperature increase may negatively affect the quality of the extracted product, it is very important to correctly determine the electric and thermal field distribution and the development of the coupled processes over time, taking into account specific features and the changes in the structure and properties of the material being processed.

The presented investigations are focused on the modelling of the coupled time dependent electric and transient thermal field distribution in cellular material during the PEF treatment, assisting the extraction of substances from vegetable seeds tissues. The aim is deep understanding of the heat transfer mechanisms and evaluation of the heat effects like local thermal spots and high values of temperature gradients. It is of interest because, on one hand, the presence of such phenomena could intensify the process of electroporation by assisting the formation of pores (thereby it is useful for substances extraction), but it also could cause overheating of the treated material and deterioration of the extracted product quality.

The study is based on the coupled electric and thermal field analysis in the multicellular structure using the Finite Element Method (FEM). Numerical experiments have been made for the PEF parameters (magnitude, number and duration of electrical impulses) corresponding to those of the experimental study [45], concerning measurements of electrically assisted mass diffusion of bioactive compounds from various vegetable tissues. Two steps have been considered in the modeling: before and after electroporation. The field analysis after electroporation is carried out for correspondingly changed size and properties of the contact area between the cells.

The analysis of the obtained results can be used for determination and adjustment of the PF parameters in order to improve the yield of the extracted substances, without risk of overheating and degrading the quality of extracted product. Later it can serve as a prerequisite for minimizing of the risk of overheating and a base for optimal control of the processes.

2. Structure of the investigated cellular tissue and mechanism of electroporation

2.1. Specific features of the plant cellular tissue

In general, the studied plant cellular material is a composition of multiple cells enclosed by cell membranes and walls and surrounded by extracellular material (Fig. 1). The cell membrane which has strong barrier functions concerning transfer between internal and external to the cell contents is composed of an assembly of lipids (phospholipids, glycolipids and cholesterol), carbohydrates and proteins, self-organized in a thin bilayer (double layer), just two molecules thick (about 5 nm). Cell walls, specific for plant materials, have complex macromolecular structure (cellulose, hemicellulose, and lignin) determining the shape of the cell and regulating cell-to-cell interactions. The intracellular liquid, which fills much of the cell, contains 80% water, dissolved proteins, electrolytes and forms of glucose, and is moderately conductive.

Fig. 1.

Main structural components of cellular tissue.

The extracellular liquid can be very different depending on the extracting solvent used. The fluid can vary from “dry” environment (filled with air) to “moist” environment (filled with water) and this can change its conductivity by orders depending on the water content.

In the presented investigation the studied cellular structure is considered (from an electric point of view) as consisting of two bulk conducting solutions, the intra- and extracellular solutions, separated by a thin insulating lipid bilayer. The simplified structure of the treated material, used in the modeling, is presented in Fig. 2.

Fig. 2.

Simplified model of cellular structure, used in the numerical modeling.

Table 1 presents the physical, electromagnetic and thermal properties and dimensions of the cellular tissue components applied in the study. The values have been determined on the basis of results, obtained in the experimental investigation presented in [45].

Table 1

Properties of cellular components

Parameter	Intracellular medium (cell)	Cell membrane	Cell walls	Extracellular medium
Average size, μm	50	0.005	0.5
Relative permittivity (ϵ_r)	73	3	9	80
Electrical conductivity (σ), Sm⁻¹	0.45	10⁻⁴	0.12	0.01 ÷ 2
Thermal conductivity (𝜆), Wm⁻¹ K⁻¹	0.5	0.5	0.5	0.5
Specific heat (Cp), J kg⁻¹ K⁻¹	3500	3500	2500	4180
Density (𝜌), kg m⁻³	1000	1200	1200	1000

2.2. Mechanism of electroporation

Electroporation is a phenomenon in which cell membrane permeability is increased by exposing the cell to external electric field of sufficient intensity and duration [44,48]. The change in cell membrane structure (Fig. 3) consisting of pore creation, release, and evolution [10], could be either reversible or irreversible; the latter phenomenon allows the transport of solutes across an electroporated membrane.

Fig. 3.

Changes in cell membrane structure exposed to an electric field.

When an external electric field is applied to cellular material, the opposite charges migrate and accumulate at the two interfaces (inner/outer) of the membrane itself, increasing the transmembrane potential. Under certain conditions, the integrity of the cellular membrane is temporary or permanently disturbed, and the rearrangement of the components leads to the formation of aqueous hydrophilic pores which enable to increase the ionic and molecular transport through the normally impermeable membrane. The appearance of these structural changes in the lipid bilayer causes a rapid increase of the membrane conductance and, as a result, a drop in the membrane voltage.

The kinetics and the extent of disintegration of the cellular tissue depend of many factors [29,35,36,39,46]: pulse parameters, types of cells and tissues, surrounding media, temperature etc. Typically, a threshold value of the electric field strength E is defined by the voltage at which the membrane conductivity increases due to the creation of pore(s). It has been determined based on electrical measurements of sharp changes (in orders) [34,37,39,45,49] in membrane impedance or by using the diffusion of different markers into and out of cells.

The mechanism of electroporation involves the formation and growth of hydrophilic pores in the cell membrane due to the generation of a membrane voltage of sufficient magnitude. When the transmembrane potential ΔU_m reaches a certain critical value ΔU_crit, the membrane will experience an electric field E strong enough to cause breakdown at specific points in the membrane.

For an isolated, idealized spherical cell, subject to a homogeneous external field, and having an insulating membrane (i.e., σ_m ≪ σ_cell, where σ_m and σ_cell are electric conductivities of the membrane and the cell), the Schwan equation is widely used to determine the electric field needed to achieve the critical transmembrane potential for electroporation or electrofusion [50]: $\begin{eqnarray}\displaystyle {\Delta}U_{m}=f\cdot {\alpha}\cdot E\cdot d_{cell}\cdot \cos {\theta} & & \displaystyle\end{eqnarray}$ (1) where E is the electric field strength in the region where the cell is situated, d_cell is the outer size of the cell, 𝛼 is a shape factor (0.75 for spheroid), 𝛩 is the angle measured from the center of the cell with respect to the direction of the field, and f is a factor, depending on the electric conductivity and size of the cell and membrane: $\begin{eqnarray}\displaystyle f=\left.\left(1+{\displaystyle \frac{{\sigma}_{m}}{2{\sigma}_{cell}K}}\right)\right/K & & \displaystyle\end{eqnarray}$ (2) where: $\begin{eqnarray}\displaystyle \left.K=1+k\left(2+{\displaystyle \frac{{\sigma}_{cell}}{{\sigma}_{m}}}\right)\right/4;\quad k={\displaystyle \frac{d_{cell}{\sigma}_{m}}{d_{m}{\sigma}_{cell}}}. & & \displaystyle\end{eqnarray}$ (3) For plant materials, the typical orders of magnitude are: d_cell: 10^-4--10⁻⁵ m; membrane thickness d_m of 10⁻⁸ m σ_cell and σ_m-electric conductivity of the cell and the membrane 0.1--1 S.m⁻¹ and 10^-4--10⁻⁶ S⋅m⁻¹, respectively. Under such conditions, k ≈ 10^-1--10⁻² and f ≈ 1. Because ΔU_m varies with the position on the cell membrane, the permeabilization first occurs in the zones of peak electric field values at the poles of the cell (at θ = 180°) and it can be concluded that electric field strength in plant cell membranes is increased about 10³–10⁴ times compared to the average electric field strength E in the material [34,49]. The voltage which is necessary for electroporation of the membrane is typically in the range 200 mV--1 V.

It has to be noted that since the biological tissues have no magnetic properties (the magnetic permeability for each of its components corresponds to that of vacuum), there are no magnetic phenomena during the electric field material processing.

3. Description of the studied system

The present study is based on numerical modeling of electrical and thermal processes in a part of a test sample of plant tissue exposed to pulsed electric field. The studied system consists of domain with simplified idealized structure composed of equal cylindrical cells, corresponding to the tissue sample. The voltage source applied to the electrodes of the system corresponds to the source applied in the experimental study [45].

3.1. Studied domain

The investigations of the coupled electric and thermal processes in cellular materials during the electric field treatment have been carried out on the basis of field distribution modelling in a domain, corresponding to the part of the cellular structure. Figure 2 presents the simplified geometry of the treated material used in the modelling.

In the analysis, biological tissue is considered to be composed of multiple cells. This allows considering the electro-thermal effects and structure deformations that occur during the PEF treatment, which are strongest in the areas of interaction between neighboring cells. The channels (pores) formed in the membrane because of electroporation allow exchange of intra and extracellular substances. The penetrated into the pores conductive substances change the properties of the contact zone of the membrane from non-conductive to conductive. These changes (deformations and conductive pores presence) are taken into account in the numerical modeling by appearance of a new, common for the neighboring cells conductive region (Fig. 4).

Fig. 4.

Two stages - before and after electroporation are considered by changing the dimensions (from 0.2 to 1 μm) and the properties (σ_pore) of the contact transmembrane zone.

In order to consider the development of the processes: pore generation, its expansion and transition from intact cells to cells with partially ruptured membranes, two stages have been considered in the fields modelling: before and after electroporation. They are related to the changes of contact zone dimensions (from 0.2 to 1 μm) and change in local electrical conductivity (from 10⁻⁴ to 10⁻² S/m) of the membrane pore σ_pore.

3.2. Electric field applied in the study

The used in the study electrodes are flat plates (as shown in principle in Figs 1 and 2), which create uniform electric field with a direction perpendicular to the plates. The study was carried out in case of pulsed electric field application with electric field strengths varying from 0.1 to 2 kV/cm. The number of pulses, pulse duration and amplitude of the applied voltage, have been chosen corresponding to the experiments carried out for disruption of cells and enhancement of mass transfer from various vegetable tissues. In the described in [45] experimental studies (Fig. 5), the problem of the effect of electroporation was studied indirectly --- by measuring mass transfer during and after application of electroporative pulses from different vegetal seeds, sources of small biologically active compounds (such as phenolic antioxidants and lipidic triacylglyserides). The pulsed electric field was applied in the form of rectangular mono-polar pulses, with pulse duration in the range 100–900 μs, inter-pulse duration of 75 ms, number of pulses up to 1000, and electric field strength up to 2000 V/cm.

Fig. 5.

Experimental setup.

The voltage applied in the numerical modelling is presented in Fig. 6. It consists of rectangular mono-polar pulses, with pulse duration p_w = 0.1 ms, period T = 5 ms and value V = 19 V. The pulse value has been determined to match the experimentally obtained results [45] for average electric field strength of 0, 425.10⁴ V/m and membrane voltage drop of range 1 V in case of electroporation. It corresponds to the smaller dimensions of the modelled part with respect to the dimensions of the experimentally studied sample.

Fig. 6.

Voltage applied in the numerical modelling.

4. Mathematical formulation of the problem

The studied processes are connected with coupled electric and thermal processes, combined with changes of the structure and physicochemical properties of the considered region. The investigation is based on the analysis of coupled electric and thermal field distribution, studied for the two stages, corresponding to the changes in the contact zone of cell membrane caused as result of electroporation.

The mathematical model used in modelling of the coupled electric and thermal processes is based on the equations, describing time-dependent electric field and transient thermal field.

The following dependencies, based on Maxwell’s equations and continuity equation are used to describe the time-dependent electric field with vectors of field strength E, displacement D and current density J in a region with a permittivity ϵ and conductivity σ : $\begin{eqnarray} \displaystyle \begin{array}{@{} l@{}} \mathrm{div}∼\mathbf{D}={\rho}\\ \mathrm{div}∼\mathbf{J}+{\displaystyle \frac{\partial {\rho}}{\partial t}}=0\\ \mathrm{rot}∼\mathbf{E}=0\quad \Rightarrow ∼\boldsymbol{ E}=-\mathrm{grad}\,V. \end{array} & & \displaystyle \end{eqnarray}$ (4) Taking into account that: $\begin{eqnarray}\displaystyle \begin{array}{@{}l@{}}\mathbf{D}={\varepsilon}∼\mathbf{E}\\ \mathbf{J}={\sigma}∼\boldsymbol{ E}\end{array} & & \displaystyle\end{eqnarray}$ (5) the following equation is obtained: $\begin{eqnarray} \displaystyle \mathrm{div}\left({\sigma}∼\mathrm{grad}V+{\displaystyle \frac{\partial }{\partial t}}({\varepsilon}∼\mathrm{grad}\,V)\right)=0 & & \displaystyle \end{eqnarray}$ (6) where V is electric scalar potential, σ is conductivity, ϵ- permittivity.

Fig. 7.

FEM mesh used in the modeling: a) multicellular system (150 μm × 400 μm); b) meshed network of dense packed cells (50 μm); c) transmembrane region with pore formed (blue) and overlapping parameters.

The governing equation [51] describing the transient thermal field distribution used in the study is: $\begin{eqnarray}\displaystyle {\rho}C_{p}{\displaystyle \frac{\partial T}{\partial t}}-{\nabla}\cdot (k{\nabla}T)=Q & & \displaystyle\end{eqnarray}$ (7) where T is temperature, k - thermal conductivity, 𝜌 - density, C_p- heat capacity, and Q is the heat source, determined in the electric field analysis.

Fig. 8.

Electric field distribution in the studied part of cellular material: (a) before electroporation; (b) after electroporation.

Fig. 9.

Temperature evolution before electroporation: (a) along the line of observation; (b) at the point of observation.

5. FEM simulations and results

The modeling and investigation of the coupled time dependent electric and transient temperature fields is based on the finite element analysis of fields’ distribution using COMSOL Multiphysics 5.3 software package [51]. The numerical experiments have been carried out for a part of the tissue sample and amplitude value of the applied voltage has been determined according to the dimensions of this part, corresponding to the experimental results and expression (1). The field distribution has been observed and analyzed with particular attention paid to its distribution along the special observation line and temperature evolution at observation point (marked in Fig. 1).

Fig. 10.

Electric field strength at the middle of the impulse t = 0.4 ms: (a) in the studied region; (b) in the contact zone.

Fig. 11.

Current density at the middle of the impulse t = 0.4 ms: (a) in the studied region; (b) in the contact zone.

Important feature of the presented study is the described above possibility to model the processes before and after electroporation by changing of the dimension of cells’ overlapping in transmembrane area, as well as the properties of the contact zone. The FE mesh used in the study is presented in Fig. 7. The specifics of its structure are illustrated in Fig. 7a: multicellular system (150 μm × 400 μm); Fig. 7b: meshed network of dense packed cells (50 μm); Fig. 7c: transmembrane region and parameters of overlapping.

Results of electric field distribution in the studied part of cellular material are shown in Fig. 8. The electric field strength for the stage before electroporation, when the cell membrane is intact is presented in Fig. 8a. In this case the overlapping is minimal with parameters of the contact zone: h = 0.2 μm and σ = 10⁻⁴ S/m. The electric field strength for the stage after electroporation, when the cell membrane is partially electroporated is presented in Fig. 8b. The parameters of contact zone in this case correspond to the maximal overlapping with height h = 1 μm and σ = 10⁻² S/m. As it can be seen from the fields map, the values of electric field strength (both maximum and average) before electroporation significantly exceed those after it.

In cases when during the treatment electroporation is not reached, there are no currents flowing through the treated material besause the intact non-conducting cell membrane practically does not allow current to flow. Therefore, there is no Joule losses and heating process. Illustration of this situation is Fig. 9, where the results of temperature evolution along the line and at the point of observation (defined in Fig. 3) are presented and as it can be seen there is practically no change after 1 s.

The cases where electroporation and flow of currents through the conducting channels are reached are of particular interest. The electric field distribution in the stage after electroporation at the moment t = 0.4 ms from the beginning of the pulse is illustrated in Fig. 10: in Fig. 10a - electric field strength in the investigated region, in Fig. 10b - electric field strength in the zone of contact between cells.

Current density distribution after electroporation at the same moment t = 0.4 ms from the beginning of the pulse is presented in Fig. 11: in the whole region in Fig. 11a and in the zone of contact after electroporation in Fig. 11b. As it can be seen, the electric field distribution is rather non-uniform with sharp changes namely in the area of contact between the cells. The losses caused by currents flowing in these zones are heat sources, leading to the heat processes in the tissue. A good illustration of the way in which currents flow and what is the direction of heat flow is presented in Fig. 12.

Fig. 12.

Currents and heat flow direction during the impulse presence: (a) currents flow; (b) heat flow.

Some results illustrating the study of transient thermal field distribution are presented in Figs 13–15. The distribution of the temperature in the studied region during the first impulse (at the moment t = 0.5 ms) is shown in Fig. 13a for the whole region. The temperature distribution in the zone of contact between the cells is presented in Fig. 13b. Hot spots in the area of contact between cells are clearly identified.

Fig. 13.

Temperature distribution during the impulse t = 0.5 ms: (a) in the studied region; (b) in the contact zone.

The distribution of the temperature gradient is also of interest, as it is an important factor influencing the process of electroporation. The temperature gradient at the moment t = 0.5 ms in the studied region is shown in Fig. 14a. Special attention is paid to the region of contact between the cells - transmembrane area. Figure 14b presents the temperature gradient for the zone around the contact.

Fig. 14.

Temperature gradient distribution during the impulse t = 0.5 ms: (a) in the studied region; (b) in the contact zone.

Figure 15 shows the changes in temperature distribution in the local region closed to contact zone during the first two pulses from the beginning of electric field processing. Temperature evolution during the first pulse (duration 0.9 ms, from t = 0 to t = 0.9 ms) is presented in the first row - Fig. 15a. The second row of the figure - Fig. 15b illustrates the temperature change between first and second pulse (4.1 ms duration - from t = 0.9 ms to t = 5 ms). The change in the temperature during the second pulse (duration 0.9 ms, from t = 5 ms to t = 5.9 ms) is shown in the third row - Fig. 15c.

Fig. 15.

(a) Temperature evolution in the transmembrane area during the first pulse; (b) Post-pulse temperature change in the transmembrane area between two pulses; (c) Temperature evolution in the transmembrane area during the second pulse.

The temperature evolution along the observation line during the process of electric field treatment for the time interval of first two pulses is presented in Fig. 16.

Fig. 16.

Temperature evolution along the line of observation for the time interval of first two pulses.

Temperature evolution along the observation line and temperature rise at the observation point during 200 pulses treatment is presented in Figs 17a and 17b.

Fig. 17.

Temperature evolution along the observation line and temperature rise at the observation point during 200 pulses treatment.

6. Conclusions

The work presents modeling and detailed analysis of coupled time dependent electric and transient thermal processes taking part in the electric field treatment of cellular materials for extraction of useful substances. The study is realized using finite element method applied to the coupled electro - thermal field problem. The numerical simulations have been carried out corresponding to the experimental study of electrically assisted mass diffusion of bioactive compounds from various vegetable tissues after electric treatment.

The analysis of the results shows that during application of consecutive electric pulses, the evolution of temperature distribution over time is a combination of heating and cooling processes of different time scales, and the influence of the inter-pulse duration is therefore particularly relevant. The distributions of electric and thermal fields during the pulse are non-uniform with maximum electric field and temperature at the poles of the cells and local spots are created.

The time-dependent temperature distribution clearly illustrates the resulting instantaneous micro-thermal effect. But, the temperature rise is spatially limited in hot spots which conform locally to the sites of electroporation where electrical current density reaches maximal values. Even if the numerical estimates predict relatively small temperature rise (maximal temperature of 0.1\,°C during the pulse), the internal heat generation process generates strong temperature gradients in the order of 10⁴ K/m. The maximum temperature inside the pore is dropping sharply during the first 1 ms and an almost homogeneous temperature distribution in a tissue’s volume (average temperature increase is only 0.1\,°C) can be recovered within 2 ms after pulse termination. Furthermore, as the volume of cells is much greater than that of the transmembrane region (where the heat is generated), the possibility of noticeable non-even heating due to non-uniform field distribution is negligible.

The presented modeling can be used for a more extensive study by parametric analysis of the influence of the electric pulse characteristics and concentration and the properties of the solvents used in the extraction. The obtained results are a potential basis for developing a control system and optimal management of the cellular materials processing.

Footnotes

Acknowledgements

The authors would like to thank the Research and Development Sector at the Technical University of Sofia for the financial support.

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