A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction

Ammari, Habib; Boulmier, Simon; Millien, Pierre

doi:10.1016/j.jde.2015.06.040

Cited by 14 publications

(20 citation statements)

References 40 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A robust way of solving this inverse problem is to formulate it as an optimal control problem, where the condiuctivity parameter is the control variable that drives the interior electric field close to the measured value, with dynamics governed by the conductivity PDE. Such optimal control methods has been used previously in the context of ultrasonically-induced Lorentz force electrical impedance tomography [5], magnetoacoustic tomography [6,7,38] and acousto-electric tomography (AET) [1,41]. In [5], the authors use an optimal control framework to recover the conductivity distribution from the measurements of current induced by static magnetic field through the Lorentz force.…”

Section: Introductionmentioning

confidence: 99%

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

2019

View full text Add to dashboard Cite

A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the interior electric field data corresponding to two boundary voltage measurements, where the conductivity and the electric potential are related through an elliptic PDE arising in electrical impedance tomography. Further, the objective functional consists of a L 1 regularization term that promotes sparsity patterns in the conductivity and a Perona-Malik anisotropic diffusion term that enhances the edges to facilitate high contrast and resolution. This framework is motivated by a similar recent approach to solve an inverse problem in acousto-electric tomography. Several numerical experiments and comparison with an existing method demonstrate the effectiveness of the proposed method for superior image reconstructions of a wide-variety of log-conductivity patterns.

show abstract

Section: Introductionmentioning

confidence: 99%

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

2019

View full text Add to dashboard Cite

show abstract

“…The latter, called inverse problem, consists of two steps, i.e. reconstructing the distribution of the Lorentz force divergence according to the ultrasonic signals collected by piezoelectric transducers, and finally the imaging of the electrical conductivity distribution (Ammari et al, 2015;_ Zywica, 2016). The detailed analysis of an electromagnetic induction in low-conductivity objects is very important for the next steps in the tomographic process of image reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Analytical and numerical models of the magnetoacoustic tomography with magnetic induction

Ziolkowski

Gratkowski

Zywica

2018

COMPEL

View full text Add to dashboard Cite

PurposeElectrical properties of biological tissues are known to be sensitive to physiological and pathological conditions of living organisms. For instance, human breast cancer or liver tumor cells have a significantly higher electrical conductivity than a healthy tissue. The paper aims to the new recently developed magnetoacoustic tomography with magnetic induction (MAT-MI) which can be deployed for electrical conductivity imaging of low-conductivity objects. Solving a test problem by using an analytical method is a useful exercise to check the validity of the more complex numerical finite element models. Such test problems are discussed in Chapter 3. The detailed analysis of an electromagnetic induction in low-conductivity objects is very important for the next steps in the tomographic process of image reconstruction. Finally, the image reconstruction examples for object’s complex shapes’ have been analyzed. The Lorentz force divergence reconstruction has been achieved with the help of time reversal algorithm. Design/methodology/approachIn given arrangements the magnetic field and eddy current vectors satisfy the Maxwell partial differential equations. Applying the separation of variables method analytical solutions are obtained for an infinitely long conducting cylindrical segment in transient magnetic field. A special case for such a configuration is an infinitely long cylinder with longitudinal crack. The analytical solutions are compared with those obtained by using numerical procedures. For complex shapes of the object, the MAT-MI images have been calculated with the help of the finite element method and time reversal algorithm. FindingsThe finite element model developed for a MAT-MI forward problem has been validated by analytical formulas. Based on such a confirmation, the MAT-MI complex model has been defined and solved. The conditions allowing successful MAT-MI image reconstruction have been provided taking into account different conductivity distribution. For given object’s parameters, the minimum number of measuring points allowing successful reconstruction has been determined. Originality/valueA simple test example has been proposed for MAT-MI forward problem. Analytical closed-form solutions have been used to check the validity of the made in-house finite element software. More complex forward and inverse problems have been solved using the software.

show abstract

“…The combination of the electromagnetics with the ultrasound is an emerging multiphysical field imaging with both of high contrast and high resolution, such as magneto-acoustic tomography with magnetic induction(MAT-MI) [4][5][6], microwave induced thermo-acoustic imaging(MI-TAI) [7] and magnetically mediated thermoacoustic imaging(MM-TAI) [8][9]. Thermo-acoustic imaging with the current injection is a new multi-physical field imaging method, the principle was proposed and the experiment was carried out aiming at low conductivity phantom in this paper.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study of Thermo-acoustic Imaging with the Current Injection

Li¹,

Liu²,

Song³

et al. 2018

dtetr

View full text Add to dashboard Cite

Thermo-acoustic imaging with the current injection (TAI-CI) is an emerging medical electrical parameter imaging technology for early detection of human diseases, it combines the advantages of high contrast of electrical impedance imaging and high resolution of ultrasound imaging. The principle of thermoacoustic imaging with the current injection was studied and the experimental system was established. The study results demonstrate that the joule heating is produced inside the objects by injecting current to phantom through a pair of electrodes, and an acoustic signal which involves the electrical parameter information of the objects is excited due to heat expansion. An experimental set for TAI-CI was established to detect and collect the acoustic signals from the semicircular ring gel phantom, the experiments were carried out aiming at low conductivity phantom (1S/m), the electrical parameter variation of the gel phantom was reflected through image reconstruction. The experiments verify the feasibility of the method for low conductivity medium imaging, and provides a basis for potential applications of TAI-CI in biological tissues.

show abstract

A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction

Cited by 14 publications

References 40 publications

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

Analytical and numerical models of the magnetoacoustic tomography with magnetic induction

Experimental Study of Thermo-acoustic Imaging with the Current Injection

Contact Info

Product

Resources

About