How Impedance Measurements and Imaging Can Be Used to Characterize the Conductivity of Tissues During the Workflow of an Electroporation-Based Therapy.

In this article we investigate the possibility of using needles, which the interventional radiologist inserts near a deep-seated tumor during an electroporation-based therapy, to characterize the electrical conductivity of patient's tissues. Specifically, we propose to exploit voltage/current measurements and imaging that are performed prior to the application of electroporation pulses. The approach is partly based on the concepts of electrical impedance tomography; however, imaging is used to build a specific geometric model and compensate for the lack of information resulting from the small number of electrodes available. 3D canonical and clinical examples, where a few electrodes surround a tumor, demonstrate the feasibility of this method: solving the inverse problem to estimate tissues conductivity converges in a few iterations. For a given error on the measurement, it is also possible to calculate the error on the estimated conductivities. The uncertainty error with clinical data is at best 5% for one of the tissues identified, due to the limitations of the clinical device used. Various improvements to clinical devices are discussed to make the conductivity estimation more accurate but also to extract more information.

Patch-based field-of-view matching in multi-modal images for electroporation-based ablations.

Various multi-modal imaging sensors are currently involved at different steps of an interventional therapeutic work-flow. Cone beam computed tomography (CBCT), computed tomography (CT) or Magnetic Resonance (MR) images thereby provides complementary functional and/or structural information of the targeted region and organs at risk. Merging this information relies on a correct spatial alignment of the observed anatomy between the acquired images. This can be achieved by the means of multi-modal deformable image registration (DIR), demonstrated to be capable of estimating dense and elastic deformations between images acquired by multiple imaging devices. However, due to the typically different field-of-view (FOV) sampled across the various imaging modalities, such algorithms may severely fail in finding a satisfactory solution. In the current study we propose a new fast method to align the FOV in multi-modal 3D medical images. To this end, a patch-based approach is introduced and combined with a state-of-the-art multi-modal image similarity metric in order to cope with multi-modal medical images. The occurrence of estimated patch shifts is computed for each spatial direction and the shift value with maximum occurrence is selected and used to adjust the image field-of-view. The performance of the proposed method - in terms of both registration accuracy and computational needs - is analyzed in the practical case of on-line irreversible electroporation procedures. In total, 30 pairs of pre-/per-operative IRE images are considered to illustrate the efficiency of our algorithm. We show that a regional registration approach using voxel patches provides a good structural compromise between the voxel-wise and "global shifts" approaches. The method was thereby beneficial for CT to CBCT and MRI to CBCT registration tasks, especially when highly different image FOVs are involved. Besides, the benefit of the method for CT to CBCT and MRI to CBCT image registration is analyzed, including the impact of artifacts generated by percutaneous needle insertions. Additionally, the computational needs using commodity hardware are demonstrated to be compatible with clinical constraints in the practical case of on-line procedures. The proposed patch-based workflow thus represents an attractive asset for DIR at different stages of an interventional procedure.

Mathematical modeling of the proliferation gradient in multicellular tumor spheroids.

MultiCellular Tumor Spheroids are 3D cell cultures that can accurately reproduce the behavior of solid tumors. It has been experimentally observed that large spheroids exhibit a decreasing gradient of proliferation from the periphery to the center of these multicellular 3D models: the proportion of proliferating cells is higher in the periphery while the non-proliferating quiescent cells increase in depth. In this paper, we propose to investigate the key mechanisms involved in the establishment of this gradient with a Partial Differential Equations model that mimics the experimental set-up of growing spheroids under different nutrients supply conditions. The model consists of mass balance equations on the two cell populations observed in the data: the proliferating cells and the quiescent cells. The spherical symmetry is used to rewrite the model in radial and relative coordinates. Thanks to a rigorous data postprocessing the model is then fit and compared quantitatively with the experimental quantification of the percentage of proliferating cells from EdU immunodetection on 2D spheroid cryosection images. The results of this calibration show that the proliferation gradient observed in spheroids can be quantitatively reproduced by our model.

Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation.

We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data. The paper proposes efficient numerical tools for forthcoming optimized procedures of cell transfection.

Conducting and permeable states of cell membrane submitted to high voltage pulses: mathematical and numerical studies validated by the experiments.

The aim of this paper is to present a new model of in vitro cell electropermeabilization, which describes separately the conducting state and the permeable state of the membrane submitted to high voltage pulses. We first derive the model based on the experimental observations and we present the numerical methods to solve the non-linear partial differential equations. We then present numerical simulations that corroborate qualitatively the experimental data dealing with the uptake of propidium iodide (PI) after millipulses. This tends to justify the validity of our modeling. Forthcoming work will be to calibrate the parameters of the model for quantitative description of the uptake.