A Partially Reflecting Random Walk on Spheres Algorithm for Electrical Impedance Tomography

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance of the new estimator both theoretically and experimentally. In a second step, the variance is considerably reduced via a novel control variate conditional sampling technique

Regional admittivity reconstruction with multi-frequency complex admittance data using contactless capacitive electrical tomography

Tomographic imaging of the electrical properties distribution within biological subjects such as the human body has been an active research goal in electrical tomography (ET). As the electrical properties of a living tissue vary with the excitation frequency, measuring the frequency-dependent behaviour of the effective dielectric can increase the possibilities for tissue characterisation, and thus enhance the potential for extended clinical applications. The ET system generally enables to capture the changes in effective dielectric properties at low spatial resolution, therefore, the complete complex admittance spectrum can be reconstructed by ET to enrich the information content and further provide better diagnostic. In this work, we demonstrate a novel contactless ET system which relies on the capacitive coupled principle, the capacitive coupled electrical tomography (CCET). Except the non-contact measuring characteristic, the capacitance-based imaging principle enables the system to obtain the measurements at higher excitation frequencies. These characteristics give CCET great potential in future medical application, as the high-frequency component of complex impedance plays a dominant role in establishing the link between the microscopic cell structures and the macroscopic admittivity images obtained from multi-frequency ET systems. In this paper, we used multi-frequency electrical signals from 320 kHz to 14 MHz to conduct the single and multiple inclusions test with different biological samples. Both the reconstructed tomographic images and the Cole-Cole plots confirm the ability of CCET in characterising different objects.</p

Low Frequency Bio-Electrical Impedance Mammography and Dielectric Measurement

Assessment of electrical impedance of biological tissues at low frequencies offers a great potential for a safe, simple, and low-cost medical breast imaging techniques such as mammography. As such, in this dissertation a mammography method which uses tissue electrical impedance to detect breast malignancies was developed. The dissertation also introduces a new technique for measuring the dielectric properties of biological tissues at low frequencies. The impedance mammography technique introduced in this study is founded on the assumption that dielectric values of breast malignancies are significantly higher than the dielectric values of normal breast tissues. While previous studies have shown that this assumption is valid at high frequencies (50MHz-20GHz), less research efforts have been dedicated to ascertain the validity of such assumption at low frequencies (in silico and tissue mimicking phantom studies. Results of this investigation suggest that imaging the electrical impedance properties of biological tissues through the proposed electrical impedance mammography can be potentially employed for breast cancer detection in a reliable and safe manner

Contribution to the Design AND Implementation of a Microwave Tomography System for Breast Cancer Detection

Abstract This thesis represents a contribution to the design and implementation of a microwave tomography system applied to breast cancer detection. Microwave tomography is an imaging technique that aims to reconstruct the permittivity and conductivity of an unknown object from measurements of its scattered field. This technique has been used in a variety of applications such as non-destructive testing, geophysical surveys and biomedical imaging. Here, we will concentrate in the breast cancer detection, where this technique has received a lot of attention in the recent years. A microwave tomography system usually involves two separate parts, a measurement system capable of performing accurate measurements of the scattered field and a set of algorithms for solving the inverse problem of retrieving the permittivity and conductivity spatial distribution of the unknown object from the scattered field measurements. This inverse problem is particularly difficult to solve, since it is non-linear and ill posed. In order to achieve a good reconstruction of the object, we need to illuminate it under several independent conditions, such as different antenna positions, frequencies or polarizations. In this thesis, we concentrate in the design of an efficient illumination configuration that tries to maximize the quality of the reconstructed images. After a literature review, it is observed that most of the proposed measurement systems share a common configuration, where in order to maximize the comfort of the patient; the antennas are arranged in a cylindrical or hemi-spherical configuration. On the other hand, the most popular method for breast cancer detection is mammography, where an X-ray image of the compressed breast at two different projections is performed. Taking this into account, two alternative configurations based on a compression of the breast are proposed, the camera and waveguide configurations. The main hypothesis behind this proposition is that a compression of the breast will allow placing the receivers very close to the breast where it is possible to measure the evanescent component of the scattered field and thus allow an enhancement of the quality of the reconstructed images. In order to prove this hypothesis, a rigorous study of the proposed configurations against a classical circular tomography setup is performed, and we determine under what conditions the reconstructed images can be enhanced. Next, the placement of the receiving antennas very close to the object under test, poses some challenges for an accurate measurement of the scattered fields, since the measurement probe itself can distort the quantity to be measured. For this purpose, an enhanced version of a previously designed near-field probe based on the modulated scattering technique is designed and validated. The probe is then used in the practical implementation of the proposed waveguide configuration. polarisations à l’intérieur du guide d’onde.----------Résumé Cette thèse représente une contribution à la conception et mise en œuvre d’un système de tomographie micro-onde pour la détection du cancer du sein. La tomographie micro-onde est une technique d’imagerie donc le but est de reconstruire la permittivité et la conductivité d’un objet inconnu à partir des mesures du champ diffusé par l’objet. Cette technique a été utilisée dans une variété d'applications comme le control non-destructif, la géophysique et l’imagerie biomédicale. Dans cette thèse, l'emphase sera mise sur la détection du cancer du sein, où cette technique a reçu énormément d’attention dans les années précédentes. Un système de tomographie micro-onde est normalement composé de deux parties séparées; un système de mesures capable de fournir des mesures précises du champ diffusé et une série d’algorithmes capable de retrouver la distribution spatiale de la permittivité et la conductivité de l’objet inconnu à partir des mesures du champ diffusé. Ce problème inverse est particulièrement difficile à résoudre, puisqu’il est non-linéaire et mal posé. Dans le but d’obtenir une bonne reconstruction de l’objet, il est nécessaire d’illuminer l’objet sous une série de conditions indépendantes, comme différentes positions d’antenne, des fréquences ou des polarisations. Dans cette thèse, l'emphase sera mise sur la conception d’une configuration d’illumination efficace qui essaie de maximiser la qualité des images reconstruites. Après une revue de littérature, on observe que la plupart des systèmes de mesures partagent une configuration commune o\`u les antennes sont placées sur une configuration cylindrique ou hémisphérique pour maximiser le confort de la patiente. D’un autre coté, la méthode la plus populaire pour le dépistage du cancer du sein est la mammographie, o\`u on utilise une image à rayons X du sein compressé en deux projections. En prenant compte de ce fait, on propose deux configurations alternatives basées sur la compression du sein, les configurations caméra et guide d’onde. L’hypothèse derrière cette proposition est que la compression du sein permet de placer les capteurs très près de ce dernier donc il est possible de mesurer la composante évanescente du champ diffusé, ce qui pourrait permettre l'amélioration de la qualité des images reconstruites. Afin de prouver cette hypothèse, une étude rigoureuse des configurations proposées et sa comparaison avec une configuration classique de tomographie circulaire est réalisée. Grace à cette étude on détermine les conditions qui permettent d’améliorer les images reconstruites. Le placement des capteurs très proche de l’objet sous test représente un défi pour une mesure précise des champs diffusés, puisque le capteur lui-même peut perturber le signal à mesurer. Pour cette raison, une version améliorée d’une sonde de mesure en champ proche basé sur la technique de diffusion modulée est conçue et validée. La sonde est utilisée pour la mise en œuvre de la configuration guide d’onde proposée. Un réseau d’antennes est développé pour l’excitation de différents modes avec différente

Investigation of 3D electrical impedance mammography systems for breast cancer detection

Breast cancer is a major disease in women worldwide with a high rate of mortality, second only to lung cancer. Hence, there is considerable interest in developing non-invasive breast cancer detection methods with the aim of identifying breast cancer at an early stage, when it is most treatable. Electrical impedance mammography (EIM) is a relatively new medical imaging method for breast cancer detection. It is a safe, painless, non-invasive, non-ionizing imaging modality, which visualizes the internal conductivity distribution of the breast under investigation. Currently some EIM systems are in clinical trials but not commercialized, as there are still many challenges with sensitivity, spatial resolution and detectability. The research in this thesis aims to enhance and optimize EIM systems in order to address the current challenges. An enhanced image reconstruction algorithm using the duo-mesh method is developed. Both in simulations and real cases of phantoms and patients, the enhanced algorithm has proven more accurate and sensitive than the former algorithm and effective in improving vertical resolution for the EIM system with a planar electrode array. To evaluate the performance of the EIM system and the image reconstruction algorithms, an image processing based error analysis method is developed, which can provide an intuitive and accurate method to evaluate the reconstructed image and outline the shape of the object of interest. Two novel EIM systems are studied, which aim to improve the spatial resolution and the detectability of a tumour deep in the breast volume. These are: rotary planar-electrode-array EIM (RPEIM) system and combined electrode array EIM (CEIM) system. The RPEIM system permits the planar electrode array to rotate in the horizontal plane, which can dramatically increase the number of independent measurements, hence improving the spatial resolution. To support the rotation of the planner electrode array, a synchronous mesh method is developed. The CEIM system has a planar electrode array and a ring electrode array operated independently or together. It has three operational modes. This design provides enhanced detectability of a tumour deep within the tissue, as required for a large volume breast. The studies of the RPEIM system and the CEIM system are based on close-to-realistic digital breast phantoms, which comprise of skin, nipple, ducts, acini, fat and tumour. This approach makes simulations very close to a clinical trial of the technology