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

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Abstract

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.

Introduction

In the last 2 years, promising results for a new non-viral efficient gene therapy have been obtained in in vivo DNA electrotransfer studies [1], [2], [3], [4], [5], [6], [7], [8]. It is also important to note that, recently, drug delivery using electric pulses has entered an active period of clinical trials [9], [10], [11], [12], [13]. These two new therapeutical approaches are based on cell electropermeabilisation, also termed electroporation, a phenomenon where a transiently increased plasma membrane permeability is obtained after the cells were exposed to short and intense electrical pulses. Electropermeabilisation thus allows otherwise non-permeant molecules to enter the cytosol [14], [15].

For effective drug delivery and gene transfection in vivo, the knowledge of electric field distribution is of utmost importance, to obtain an effective permeabilisation as well as to maintain the viability of the electropermeabilised cells. Indeed, in order to achieve electropermeabilisation in the tissue of interest, the magnitude of electric field intensity has to be above a critical threshold value [14], [16], [17], i.e. the reversible threshold. Furthermore, the magnitude of electric field intensity should not exceed the value which would produce irreversible damage to the plasma membrane, i.e. the irreversible threshold. Thus, the magnitude of electric field intensity should be high enough to cause reversible electropermeabilisation, but lower than the value causing irreversible damage [2], [18]. The latter is the most critical for in vivo gene transfer, but is also desirable in electrochemotherapy in order not to produce large instantaneous necrosis, which would result in massive tumour necrosis and possible ulceration and wound appearance. Moreover, for gene therapy, it has been recently reported [19] that, under relatively homogeneous exposure conditions [20], the optimal conditions for gene transfer correspond to the use of long pulses (20 ms) at a voltage just necessary to obtain cell electropermeabilisation, i.e. just above the reversible permeabilisation threshold. Above the irreversible permeabilisation threshold, when permanent damage is inflicted on the plasma membrane, viability is lost and efficacy of the DNA transfer is severely impaired [2]. Therefore it was necessary to determine (1) the electric field distribution in the target tissues, (2) the reversible as well as (3) the irreversible permeabilisation thresholds in order to use voltages and electrode geometries resulting in optimal exposure of the targeted tissue to electric fields intensities comprised between the two thresholds.

Very few studies have dealt with these questions. In ex vivo experiments, using two parallel plates separated by 2 mm, that represents a rather homogeneous exposure system, a variable threshold (ranging from 300 to 500 V/cm) was found for a fibrosarcoma tumour exposed to eight pulses of 100 ms at a frequency of 1 Hz [21]. Recently, using a numerical two-dimensional model for electric field distribution, parallel plates as electrodes, and a quantitative Cr51-EDTA uptake assay, threshold for reversible in vivo permeabilisation of mouse skeletal muscle was found at 450 V/cm for the same type of pulses [20]. This work also revealed that the field generated by needle electrodes was not homogeneous and that both the numerical two-dimensional model as well as a global uptake assay were not precise enough, using needle electrodes, for detailed three-dimensional studies of the field distribution in vivo and for threshold determinations. Thus it was necessary to build a detailed three-dimensional model to go further in the understanding and optimisation of electrochemotherapy and gene electrotransfer in vivo.

It seemed also necessary to use new permeabilisation tests giving topological information on electropermeabilisation occurrence with respect to electrode positioning. Therefore a new test was set to perform our work (H. Mekid et al., in preparation) based on the rapid morphological changes produced by the entry of bleomycin into the electropermeabilised cells [22], [23].

Needle electrodes seem to be the most practical type of electrodes for clinical applications of both electrochemotherapy and DNA electrotransfer for gene therapy. However, the field generated by two or more needles is very inhomogeneous, as compared to the field distribution between two parallel plates. Nevertheless, it has been previously demonstrated that electric field distribution in the tissue can be controlled by the position of the electrodes in the tissue [24], [25], [26]. It was also shown that electrode geometry influences electric field distribution in the tissue and this parameter was taken into account when the work here reported was prepared.

For effective drug delivery after electric pulse application, all the authors have consistently used the same conditions (six or eight pulses of variable voltage-to-distance ratio (usually 1300 V/cm) and of 100 μs delivered at a frequency of 1 Hz) as initially determined by Mir et al. [27]. For in vivo DNA electrotransfer for gene therapy purposes, the electrical parameters have not yet been homogenised: in particular, electric pulse length may vary from 100 μs to 10, 20 or even 50 ms [1], [2], [3], [4], [5], [6], [7], [8], [28], [29]. Therefore, when it was necessary to fix the experimental conditions for the validation of our tri-dimensional numerical model, the most representative conditions were chosen, i.e. those already used in the clinical settings for electrochemotherapy (pulses of 100 μs). Finally, voltages at which effective either drug delivery or gene electrotransfer were obtained for a given electrode geometry have been determined in vivo [1], [2], [3], [4], [21], [30], [31], [32], but until now, the determination of the threshold magnitudes of electric field intensity for reversible and irreversible electropermeabilisation in tissue has not been reported. To find the ways for precise determinations of these thresholds was also one of the objectives of this paper.

Thus, in the present article, we report the construction of a three-dimensional finite element model in order to determine electric field distribution around and between needle electrodes for a homogeneous and isotropic tissue. The results obtained by the numerical model were then tested in liver tissue in in vivo conditions using parameters widely used in clinical applications (eight electric pulses of 100 μs delivered at 1 Hz). In the numerical model, liver was represented as a parallelepiped of homogenous and isotropic conductor. We used two parallel needles as electrodes and studied the influence of electrode diameter on electric field distribution. Both reversible and irreversible electropermeabilisation thresholds for normal rabbit liver cells in vivo were experimentally determined using qualitative tests that allow to visualise the actual geometry of the electric field in vivo and to validate our numerical model.

Section snippets

Animals

New Zealand white rabbits (Elevage Scientifique des Dombes, Romans, France) were maintained under standard conditions with laboratory diet and water ad libitum. Altogether, 22 rabbits were used in this study. All procedures were carried out under general anaesthesia using intravenous ketamine hydrochloride (Ketamine, Parke Davis, Courbevoie, France) and xylazine 2% (Rompun, Bayer, Puteaux, France). At the end of the experiment, rabbits were killed by an intravenous overdose of Pentobarbital

Hepatocyte diameter determination

The inner distance between the electrodes was determined in histological sections based on Indian ink marks and was found to be 7.9±0.8 mm. Since the two needles used as electrodes were separated by 8 mm (see Section 2), this experimentally determined value demonstrated that no significant distortion of the sample was caused by handling of tissue samples during preparation for histological observation. Consequently, much confidence could be put on the topological observations made on the

Discussion

We report here the first determinations of in vivo permeabilisation thresholds and the corresponding transmembrane voltages at these thresholds based on three-dimensional model of electric field distribution in liver, and the corresponding biological experimental observations that validated the three-dimensional model. The model predicted, and the in vivo experiments confirmed, that electric field distribution depended on the diameter of the electrodes (Fig. 2). Electrodes with smaller diameter

Acknowledgements

This research was partially supported by the CNRS and IES, Ministry of Science and Technology of the Republic of Slovenia and PROTEUS Programme of cooperation between France and Slovenia. The authors are indebted to Dr. Yoko Kubota and Mrs. Nawel Mahrour for blind examination of histological sections, to Dr. Dong-Jian An, Dr. Gabriel Bindoula, Dr. Patrice Ardouin, Mr. Fabrice Hérant and Miss Annie Rouchès for their valuable help during various phases of the study. We would also like to thank

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