Applications de la force de Lorentz en acoustique médicale

The ability of the Lorentz force to link a mechanical displacement to an electrical current presents a strong interest for medical acoustics, and three applications were studied in this thesis. In the first part of this work, a hydrophone was developed for mapping the particle velocity of an acoustic field. This hydrophone was constructed using a thin copper wire and an external magnetic field. A model was elaborated to determine the relationship between the acoustic pressure and the measured electrical current, which is induced by Lorentz force when the wire vibrates in the acoustic field of an ultrasound transducer. The built prototype was characterized and its spatial resolution, frequency response, sensitivity, robustness and directivity response were investigated. An imaging method called Lorentz Force Electrical Impedance Tomography was also studied. In this method, a biological tissue is vibrated by ultrasound in a magnetic field, which induces an electrical current by Lorentz force. The electrical impedance of the tissue can be deduced from the measurement of the current. This technique was applied for imaging a gelatin phantom, a beef muscle sample, and a thermal lesion in a chicken breast sample. This showed the method may be useful for providing additional contrast to conventional ultrasound imaging. Finally, this thesis demonstrated that shear waves can be generated in soft tissues using Lorentz force. This work was performed by applying an electrical current with two electrodes in a soft solid placed in a magnetic field. Shear waves were observed in gelatin phantom and liver sample. The speed of the shear waves were used to compute elasticity and their source to map the electrical conductivity of the samplesLa capacité de la force de Lorentz à relier un déplacement mécanique à un courant électrique présente un intérêt certain pour l'acoustique médicale, et trois applications ont été étudiées dans cette thèse. Dans la première partie de ce travail, un hydrophone a été développé pour effectuer des champs de vitesse acoustique. Cet hydrophone était constitué d'un fil de cuivre vibrant dans un champ magnétique. Un modèle a été élaboré pour déterminer une relation entre la pression acoustique et le courant électrique mesure, qui est induit par force de Lorentz lorsque le fil vibre dans un champ acoustique. Un prototype a ensuite été conçu et sa résolution spatiale, sa réponse fréquentielle, sa sensibilité, sa résistance et sa réponse directionnelle ont été examinées. Une méthode d'imagerie appelée Tomographie d'Impedance Electrique par Force de Lorentz a aussi été étudiée. Dans cette méthode, un tissu biologique est déplacé par ultrasons dans un champ magnétique, ce qui induit un courant électrique par force de Lorentz. L'impédance électrique du tissu peut ensuite être déduite de la mesure du courant. Cette technique a été appliquée pour réaliser des images d'un fantôme de gélatine, d'un muscle de bœuf, et d'une lésion thermique dans un échantillon de poulet. Cela a montré que la méthode est potentiellement utile pour fournir un contraste supplémentaire à des images ultrasonores classiques. Enfin, cette thèse a démontré que des ondes de cisaillement peuvent être générées dans des tissus mous par force de Lorentz. Cela a été réalisé en appliquant un courant électrique par deux électrodes dans un solide mou place dans un champ magnétique. Des ondes de cisaillement ont été observées dans des échantillons de gélatine et de foie. La vitesse des ondes de cisaillement a été utilisée pour calculer l'élasticité et leur source pour cartographier la conductivité électrique des échantillon

Lorentz Force Electrical Impedance Tomography

This article describes a method called Lorentz Force Electrical Impedance Tomography. The electrical conductivity of biological tissues can be measured through their sonication in a magnetic field: the vibration of the tissues inside the field induces an electrical current by Lorentz force. This current, detected by electrodes placed around the sample, is proportional to the ultrasonic pressure, to the strength of the magnetic field and to the electrical conductivity gradient along the acoustic axis. By focusing at different places inside the sample, a map of the electrical conductivity gradient can be established. In this study experiments were conducted on a gelatin phantom and on a beef sample, successively placed in a 300 mT magnetic field and sonicated with an ultrasonic transducer focused at 21 cm emitting 500 kHz bursts. Although all interfaces are not visible, in this exploratory study a good correlation is observed between the electrical conductivity image and the ultrasonic image. This method offers an alternative to detecting pathologies invisible to standard ultrasonography

A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography

We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force. This current can be detected by electrodes placed around the tissue; it is proportional to the velocity of the ultrasonic pulse, but depends nonlinearly on the conductivity distribution. The imaging problem is to reconstruct the conductivity distribution from measurements of the induced current. To solve this nonlinear inverse problem, we first make use of a virtual potential to relate explicitly the current measurements to the conductivity distribution and the velocity of the ultrasonic pulse. Then, by applying a Wiener filter to the measured data, we reduce the problem to imaging the conductivity from an internal electric current density. We first introduce an optimal control method for solving such a problem. A new direct reconstruction scheme involving a partial differential equation is then proposed based on viscosity-type regularization to a transport equation satisfied by the current density field. We prove that solving such an equation yields the true conductivity distribution as the regularization parameter approaches zero. We also test both schemes numerically in the presence of measurement noise, quantify their stability and resolution, and compare their performance

Contactless Remote Induction of Shear Waves in Soft Tissues Using a Transcranial Magnetic Stimulation Device

This study presents the first observation of shear wave induced remotely within soft tissues. It was performed through the combination of a transcranial magnetic stimulation device and a permanent magnet. A physical model based on Maxwell and Navier equations was developed. Experiments were performed on a cryogel phantom and a chicken breast sample. Using an ultrafast ultrasound scanner, shear waves of respective amplitude of 5 and 0.5 micrometers were observed. Experimental and numerical results were in good agreement. This study constitutes the framework of an alternative shear wave elastography method

Imaging of Shear Waves Induced by Lorentz Force in Soft Tissues

This study presents the first observation of elastic shear waves generated in soft solids using a dynamic electromagnetic field. The first and second experiments of this 5 study showed that Lorentz force can induce a displacement in a soft phantom and that this displacement was detectable by an ultrasound scanner using speckle-tracking algorithms. For a 100 mT magnetic field and a 10 ms, 100 mA peak-to-peak electrical burst, the displacement reached a magnitude of 1 um. In the third experiment, we showed that Lorentz force can induce shear waves in a phantom. A physical model 10 using electromagnetic and elasticity equations was proposed. Computer simulations were in good agreement with experimental results. The shear waves induced by Lorentz force were used in the last experiment to estimate the elasticity of a swine liver sample

Acousto-electrical speckle pattern in Lorentz force electrical impedance tomography

Ultrasound speckle is a granular texture pattern appearing in ultrasound imaging. It can be used to distinguish tissues and identify pathologies. Lorentz force electrical impedance tomography is an ultrasound-based medical imaging technique of the tissue electrical conductivity. It is based on the application of an ultrasound wave in a medium placed in a magnetic field and on the measurement of the induced electric current due to Lorentz force. Similarly to ultrasound imaging, we hypothesized that a speckle could be observed with Lorentz force electrical impedance tomography imaging. In this study, we first assessed the theoretical similarity between the measured signals in Lorentz force electrical impedance tomography and in ultrasound imaging modalities. We then compared experimentally the signal measured in both methods using an acoustic and electrical impedance interface. Finally, a bovine muscle sample was imaged using the two methods. Similar speckle patterns were observed. This indicates the existence of an "acousto-electrical speckle" in the Lorentz force electrical impedance tomography with spatial characteristics driven by the acoustic parameters but due to electrical impedance inhomogeneities instead of acoustic ones as is the case of ultrasound imaging

A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography

We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force. This current can be detected by electrodes placed around the tissue; it is proportional to the velocity of the ultrasonic pulse, but depends nonlinearly on the conductivity distribution. The imaging problem is to reconstruct the conductivity distribution from measurements of the induced current. To solve this nonlinear inverse problem, we first make use of a virtual potential to relate explicitly the current measurements to the conductivity distribution and the velocity of the ultrasonic pulse. Then, by applying a Wiener filter to the measured data, we reduce the problem to imaging the conductivity from an internal electric current density. We first introduce an optimal control method for solving such a problem. A new direct reconstruction scheme involving a partial differential equation is then proposed based on viscosity-type regularization to a transport equation satisfied by the current density field. We prove that solving such an equation yields the true conductivity distribution as the regularization parameter approaches zero. We also test both schemes numerically in the presence of measurement noise, quantify their stability and resolution, and compare their performance. © 2014 Elsevier Masson SAS

Electromagnetic Hydrophone with Tomographic System for Absolute Velocity Field Mapping

The velocity and pressure of an ultrasonic wave can be measured by an electromagnetic hydrophone made of a thin wire and a magnet. The ultrasonic wave vibrates the wire inside a magnetic field, inducing an electrical current. Previous articles reported poor spatial resolution of comparable hydrophones along the axis of the wire. In this study, submillimetric spatial resolution has been achieved by using a tomographic method. Moreover, a physical model is presented for obtaining absolute measurements. A pressure differential of 8% has been found between piezoelectric and electromagnetic hydrophone measurements. These characteristics show this technique as an alternative to standard hydrophones