A validated model of in vivo electric field distribution in tissues for electrochemotherapy and for DNA electrotransfer for gene therapy.

Permeabilising electric pulses can be advantageously used for DNA electrotransfer in vivo for gene therapy, as well as for drug delivery. In both cases, it is essential to know the electric field distribution in the tissues: the targeted tissue must be submitted to electric field intensities above the reversible permeabilisation threshold (to actually permeabilise it) and below the irreversible permeabilisation threshold (to avoid toxic effects of the electric pulses). A three-dimensional finite element model was built. Needle electrodes of different diameters were modelled by applying appropriate boundary conditions in corresponding grid points of the model. The observations resulting from the numerical calculations, like the electric field distribution dependence on the diameter of the electrodes, were confirmed in appropriate experiments in rabbit liver tissue. The agreement between numerical predictions and experimental observations validated our model. Then it was possible to make the first precise determination of the magnitude of the electric field intensity for reversible (362+/-21 V/cm, mean +/- S.D.) and for irreversible (637+/-43 V/cm) permeabilisation thresholds of rabbit liver tissue in vivo. Therefore the maximum of induced transmembrane potential difference in a single cell of the rabbit liver tissue can be estimated to be 394+/-75 and 694+/-136 mV, respectively, for reversible and irreversible electroporation threshold. These results carry important practical implications.

Numerical modeling for in vivo electroporation.

Electropermeabilization of cell plasma membrane is a threshold phenomenon. When a cell is exposed to electric field a spatially dependent transmembrane potential is induced (1). Above a certain threshold value of transmembrane potential permeability of plasma membrane drastically increases. Thus, in order to obtain plasma membrane permeabilization an above threshold transmembrane potential needs to be obtained. This is achieved by an above threshold electric field intensity. Electropermeabilization is therefore characterized by electric field intensity, but also by the duration and number of applied pulses, as well as their shape (2). Electric field intensity of the pulses of selected duration must reach a threshold, typical for a particular type of cell (3). This threshold is also different for the cells in tissue compared to the threshold for electropermeabilization of the membrane of isolated cells (4). Selected electric field intensity, appropriate for electroporation, should at the same time not exceed the value which will cause irreversible permeabilization or even death of the cell (5). This is particularly important for electro-gene transfection.

Calculation of the electrical parameters in electrochemotherapy of solid tumours in mice.

Electrochemotherapy is a novel approach in chemotherapeutic drug delivery into tumours. Short intense direct current electric pulses are applied to tumour tissue causing electropermeabilisation thus enabling entrance of chemotherapeutic drugs into cells which otherwise do not easily penetrate. A three dimensional anatomically based finite element model of the mouse with injected subcutaneous solid tumour was built. The main goal of the study was to evaluate the influence of the electrode orientation on the distribution of electric field in the tumour and surrounding tissue during electrochemotherapy. Two electrode configurations, previously examined in experimental study, were modelled. Electric field distributions were calculated for each configuration. The main conclusion of our study is that changing electrode orientation strongly influences the distribution of the electric field inside the tumour in the electrochemotherapy of solid tumours in mice, which is in good agreement with the results of the experimental study. The efficacy of the electrochemotherapy depends on the magnitude of the electric field intensity inside tumour tissue.

The importance of electric field distribution for effective in vivo electroporation of tissues.

Cells exposed to short and intense electric pulses become permeable to a number of various ionic molecules. This phenomenon was termed electroporation or electropermeabilization and is widely used for in vitro drug delivery into the cells and gene transfection. Tissues can also be permeabilized. These new approaches based on electroporation are used for cancer treatment, i.e., electrochemotherapy, and in vivo gene transfection. In vivo electroporation is thus gaining even wider interest. However, electrode geometry and distribution were not yet adequately addressed. Most of the electrodes used so far were determined empirically. In our study we 1) designed two electrode sets that produce notably different distribution of electric field in tumor, 2) qualitatively evaluated current density distribution for both electrode sets by means of magnetic resonance current density imaging, 3) used three-dimensional finite element model to calculate values of electric field for both electrode sets, and 4) demonstrated the difference in electrochemotherapy effectiveness in mouse tumor model between the two electrode sets. The results of our study clearly demonstrate that numerical model is reliable and can be very useful in the additional search for electrodes that would make electrochemotherapy and in vivo electroporation in general more efficient. Our study also shows that better coverage of tumors with sufficiently high electric field is necessary for improved effectiveness of electrochemotherapy.