Magnetoacoustic tomography with magnetic induction for imaging electrical impedance of biological tissue

Abstract

An experimental feasibility study was conducted on Magnetoacoustic-Tomography with Magnetic Induction (MAT-MI). It is demonstrated that the 2-dimensional (2D) MAT-MI system can detect and image the boundaries between regions of different electrical conductivity with high spatial resolution. Utilizing a magnetic stimulation coil, MAT-MI evokes magnetically induced eddy current in an object which is placed in a static magnetic field. Because of the existence of Lorenz forces, the eddy current in turn causes acoustic vibrations, which are measured around the object in order to reconstruct the electrical impedance distribution of the object. The present experimental results from the saline and gel phantoms are promising and suggest the merits of MAT-MI in imaging electrical impedance of biological tissue with high spatial resolution.Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) is an imaging modality combining pulsed magnetic stimulation with sonography and it is proposed for imaging the electrical impedance of samples noninvasively 1 . Noninvasive measurement of electrical properties of biological tissue has drawn substantial research interest for decades and a variety of techniques has been developed such as Electrical impedance tomography (EIT) 2-4 , Magnetic Resonance Electrical Impedance Tomography (MREIT) 5-7 , and Magnetic Induction Tomography (MIT) 8, 9 . In addition, Magnetoacoustic Tomography (MAT) 10, 11 and Hall Effect Imaging (HEI) 12, 13 have both been reported for combining bioelectromagnetism together with sonography.In the MAT-MI approach we investigated here, pulsed magnetic stimulation (μs) is imposed on an object placed in a static magnetic field. The magnetically induced eddy current is then subject to Lorenz force. The Lorenz force causes acoustic vibrations which can be measured to reconstruct the conductivity distribution of the sample. Denoting the static magnetic field as B 0 , the magnetically induced current density distribution as J̃ (the tilt over a variable indicates a function of time; otherwise, the variable is not a function of time if not denoted explicitly), the Lorenz force can be described as J̃ × B 0 . The wave equation governing the pressure distribution p̃ can be written in equation (1) 11 (1) NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscriptwhere c s is the acoustic speed in the media. In equation (1), J(r, t) = J(r)δ(t), with an assumption that the induced eddy current has an ideal pulsed distribution over time. This would be a reasonable approximation as long as the excitation coil is sending pulse stimulations that are short enough. Using Green's function, the solution of equation (1) can be written as in (2): (2) where R = |r − r′|, and V is the volume containing the acoustic source. The pressure on a surface surrounding the object can be measured to reconstruct the source term ∇ · (J × B 0 ) using the time reversing technique 1, 14 as in equation (3):where r d is a point on the detection surface Σ, n is the normal vector of...

Mathematical models and reconstruction methods in magneto-acoustic imaging

“…The resulting pressure or tissue displacement contains information about the action current distribution. Let z ∈ Ω be the location of an electric dipole, which represents an active nerve or muscle fiber, with strength c. The wave equation governing the induced pressure distribution p z can be written as 12) for some final observation time T , where c s is the acoustic speed in Ω. The pressure satisfies the Dirichlet boundary condition (2.9) and the initial conditions (2.10).…”

“…We refer the reader to [14,12,13,17,18,8,15,16] for physical basic principles of vibration potential tomography, magneto-acoustic tomography with magnetic induction, and magneto-acoustic current imaging.…”

Magnetoacoustic tomography with current injection

“…However, if the resultant signals w(r,t) are used, which are collected from various directions of the transducers, a 2-D image can be reconstructed. The acoustic source term (3) can be obtained by the means of the simplified back projection algorithm for acoustic sources [25,26].…”

“…He group [13] derived the formulae for the forward problem and the inverse problem, and studied conductivity reconstruction of MAT-MI [14]. Experimental studies were also carried out on copper loops [9], gel phantoms [11] and salted tissue samples [13]. Research at the Institute of Electrical Engineering, Chinese Academy of Sciences published their findings on the mechanism of sound source and to propose three methods to avoid the singularity of the divergence of Lorentz force on the interface between two mediums [15][16][17].…”

“…MAT includes magneto-acoustic tomography with magnetic induction (MAT-MI) [10][11][12][13] and magneto-acoustic tomography with current injection (MAT-CI). MAT-MI uses magnetic induction to induce eddy currents in the conductive sample and generates acoustic vibrations through the Lorentz force coupling mechanism, which was proposed by He group [9] in 2005.…”