Electrical Conductivity Of Biological Tissues Research Articles

Multiscale Analysis of Composite Structures

The goal of this paper is to present some homogenization results for diffusion problems in composite structures, formed by two media with different features. Our setting is relevant for modeling heat diffusion in composite materials with imperfect interfaces or electrical conduction in biological tissues. The approach we follow is based on the periodic unfolding method, which allows us to deal with general media.

Magnetic induction spectroscopy: non-contact measurement of the electrical conductivity spectra of biological samples

Measurement of the electrical conductivity of biological tissues as a function of frequency, often termed ‘bioelectrical impedance spectroscopy (BIS)’, provides valuable information on tissue structure and composition. In implementing BIS though, there can be significant practical difficulties arising from the electrode–sample interface which have likely limited its deployment in industrial applications. In magnetic induction spectroscopy (MIS) these difficulties are eliminated through the use of fully non-contacting inductive coupling between the sensors and sample. However, inductive coupling introduces its own set of technical difficulties, primarily related to the small magnitudes of the induced currents and their proportionality with frequency. This paper describes the design of a practical MIS system incorporating new, highly-phase-stable electronics and compares its performance with that of electrode-based BIS in measurements on biological samples including yeast suspensions in saline (concentration 50–400 g l−1) and solid samples of potato, cucumber, tomato, banana and porcine liver. The shapes of the MIS spectra were in good agreement with those for electrode-based BIS, with a residual maximum discrepancy of 28%. The measurement precision of the MIS was 0.05 S m−1 at 200 kHz, improving to 0.01 S m−1 at a frequency of 20 MHz, for a sample volume of 80 ml. The data-acquisition time for each MIS measurement was 52 s. Given the value of spectroscopic conductivity information and the many advantages of obtaining these data in a non-contacting manner, even through electrically-insulating packaging materials if necessary, it is concluded that MIS is a technique with considerable potential for monitoring bio-industrial processes and product quality.

Magnetoacoustic Imaging of Electrical Conductivity of Biological Tissues at a Spatial Resolution Better than 2 mm

Magnetoacoustic tomography with magnetic induction (MAT-MI) is an emerging approach for noninvasively imaging electrical impedance properties of biological tissues. The MAT-MI imaging system measures ultrasound waves generated by the Lorentz force, having been induced by magnetic stimulation, which is related to the electrical conductivity distribution in tissue samples. MAT-MI promises to provide fine spatial resolution for biological tissue imaging as compared to ultrasound resolution. In the present study, we first estimated the imaging spatial resolution by calculating the full width at half maximum (FWHM) of the system point spread function (PSF). The actual spatial resolution of our MAT-MI system was experimentally determined to be 1.51 mm by a parallel-line-source phantom with Rayleigh criterion. Reconstructed images made from tissue-mimicking gel phantoms, as well as animal tissue samples, were consistent with the morphological structures of the samples. The electrical conductivity value of the samples was determined directly by a calibrated four-electrode system. It has been demonstrated that MAT-MI is able to image the electrical impedance properties of biological tissues with better than 2 mm spatial resolution. These results suggest the potential of MAT-MI for application to early detection of small-size diseased tissues (e.g. small breast cancer).

Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range

We derive a macroscopic model of electrical conduction in biologicaltissues in the high radio-frequency range, which is relevant in applicationslike electric impedance tomography. This model is derived via a homogenizationlimit by a microscopic formulation, based on Maxwell’s equations, takinginto account the periodic geometry of the microstructure. We also study theasymptotic behavior of the solution for large times. Our results imply thatperiodic boundary data lead to an asymptotically periodic solution.

Bestimmung der komplexen elektrischen Leitfähigkeit biologischen Gewebes mittels kontaktloser Magnetimpedanzmessung / Estimation of biological tissue conductivity with contact-free magnetic impedance measurements

At present, there are several methods that utilize electrical conductivity of biological tissue, such as biological impedance spectroscopy (BIS). Because these techniques use conductivity values for further analysis (e.g., body water distribution, etc.), accuracy of conductivity measurement is crucial. Traditionally, most impedance-based techniques rely on conductive interaction between tissue and external electrical measurement devices. Thus, electrode properties can influence the results of conductivity measurements. In this study, a contact-free measurement technique is presented, which is based on magnetic induction of eddy currents and measurement of the tiny reinduced voltages in external measurement coils. Our results indicate that it is principally possible to determine conductivity of biological tissue with this technique.

Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues

We study an electrical conduction problem in biological tissues in the radiofrequency range, which is governed by an elliptic equation with memory. We prove the time exponential asymptotic stability of the solution. We provide in this way both a theoretical justification to the complex elliptic problem currently used in electrical impedance tomography and additional information on the structure of the complex coefficients appearing in the elliptic equation. Our approach relies on the fact that the elliptic equation with memory is the homogenisation limit of a sequence of problems for which we prove suitable uniform estimates.

Stability and memory effects in a homogenized model governing the electrical conduction in biological tissues

We present a macroscopic model of electrical conduction in biological tissues. This model is derived via a homogenization limit by a microscopic formulation based on Maxwell’s equations, taking into account the periodic geometry of the microstructure. We also study the asymptotic behavior of the model for large times. Our results imply that periodic boundary data lead to an asymptotically periodic solution. The model is relevant to applications like electric impedance tomography.

Applications of homogenization techniques to the electrical conduction in biological tissues

AbstractWe study a family of problems set in a finely mixed periodic medium, modelling electrical conduction in biological tissues. We prove a unified derivation of these different schemes from the Maxwell equations in the quasi‐stationary approximation and we investigate the behaviour of the corresponding macroscopic models. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On a hierarchy of models for electrical conduction in biological tissues

AbstractIn this paper we derive a hierarchy of models for electrical conduction in a biological tissue, which is represented by a periodic array of period ε of conducting phases surrounded by dielectric shells of thickness εη included in a conductive matrix. Such a hierarchy will be obtained from the Maxwell equations by means of a concentration process η → 0, followed by a homogenization limit with respect to ε. These models are then compared with regard to their physical meaning and mathematical issues. Copyright © 2005 John Wiley & Sons, Ltd.

Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics

We study the existence and uniqueness of solutions to an elliptic problem with a nonlinear dynamic boundary condition, relating the conormal derivative of the unknown to the time derivative of its jump across an internal interface. We firstly prove the well-posedness of a suitable linear version of this problem, by means of a classical result in abstract parabolic theory; then, we study the nonlinear case using a fixed point technique. Our mathematical scheme is of interest in the modelling of electrical conduction in biological tissues.

EVOLUTION AND MEMORY EFFECTS IN THE HOMOGENIZATION LIMIT FOR ELECTRICAL CONDUCTION IN BIOLOGICAL TISSUES

We study a problem set in a finely mixed periodic medium, modelling electrical conduction in biological tissues. The unknown electric potential solves standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by a dielectric surface (the cell membranes), which exhibits both a capacitive and a nonlinear conductive behaviour. Accordingly, dynamical conditions prevail on the membranes, so that the dependence of the solution on the time variable t is not only of parametric character. As the spatial period of the medium goes to zero, the electric potential approaches in a suitable sense a homogenization limit u0, which keeps the prescribed boundary data, and solves the equation [Formula: see text]. This is an elliptic equation containing a term depending on the history of the gradient of u0; the matrices B0, A1 in it depend on the microstructure of the medium. More exactly, we have that, in the limit, the current is still divergence-free, but it depends on the history of the potential gradient, so that memory effects explicitly appear. The limiting equation also contains a term ℱ keeping trace of the initial data.

Homogenization limit for electrical conduction in biological tissues in the radio-frequency range

We study an evolutive model for electrical conduction in biological tissues, where the conductive intra-cellular and extracellular spaces are separated by insulating cell membranes. The mathematical scheme is an elliptic problem, with dynamical boundary conditions on the cell membranes. The problem is set in a finely mixed periodic medium. We show that the homogenization limit u 0 of the electric potential, obtained as the period of the microscopic structure approaches zero, solves the equation − div(σ 0∇ xu 0+A 0∇ xu 0+∫ 0 tA 1(t−τ)∇ xu 0(x,τ) dτ− F(x,t))=0 where σ 0>0 and the matrices A 0, A 1 depend on geometric and material properties, while the vector function F keeps trace of the initial data of the original problem. Memory effects explicitly appear here, making this elliptic equation of non standard type. To cite this article: M. Amar et al., C. R. Mecanique 331 (2003).