Conductivity Of Biological Tissues Research Articles

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.

Micromachined Hot-Wire Thermal Conductivity Probe for Biomedical Applications

This paper presents the design, fabrication, numerical simulation, and experimental validation of a micromachined probe that measures thermal conductivity of biological tissues. The probe consists of a pair of resistive line heating elements and resistance temperature detector sensors, which were fabricated by using planar photolithography on a glass substrate. The numerical analysis revealed that the thermal conductivity and diffusivity can be determined by the temperature response induced by the uniform heat flux in the heating elements. After calibrating the probe using a material (agar gel) of known thermal conductivity, the probe was deployed to calculate the thermal conductivity of Crisco. The measured value is in agreement with that determined by the macro-hot-wire probe method to within 3%. Finally, the micro thermal probe was used to investigate the change of thermal conductivity of pig liver before and after RF ablation treatment. The results show an increase in thermal conductivity of liver after the RF ablation.

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.

Pulse-power integrated-decay technique for the measurement of thermal conductivity

A pulse-power integrated-decay technique for the measurement of thermal conductivity of biological tissues is presented. A self-heated thermistor probe is used to deliver heat and also to measure the temperature response. Three-dimensional finite element analyses are used in this paper to design and optimize the technique. The thermal conductivity measurements from the computer simulations were in close accordance with the experimental data. An empirical calibration process, performed in glycerol and agar-gelled water, provides accurate thermal conductivity measurements. An accuracy analysis evaluated multiple experimental protocols using three solutions of known thermal properties. The results indicate that the thermal decay technique protocol had better accuracy than the constant temperature heating techniques. In vitro measurements demonstrate the variability of tissue thermal conductivity, and the need to perform direct measurements for tissues of interest. The factors that may introduce error in the experimental data are (i) poor thermal/physical contact between the thermistor probe and tissue sample, (ii) water loss from tissue during the course of experimentation and (iii) temperature stability.

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.

Magnetic stimulation of knee – mathematical model

Arthritis, the illness of the bones, is one of the diseases which especially attack the knee joint. Magnetic stimulation is a very promising treatment, although not very clear as to its physical background. Deals with the mathematical simulation of the therapeutical technique, i.e. the magnetic stimulation method. Considers the low‐frequency magnetic field. To consider eddy currents one uses the pair of potentials: electric vector potential T→ and magnetic scalar potential Ω . Since the problem is of low frequency and the electric conductivity of biological tissues is very small, consideration of electric vector potential only is quite satisfactory.

Temperature dependence of thermal conductivity of biological tissues

In this paper, we present our experimental results on the determination of the thermal conductivity of biological tissues using a transient technique based on the principles of the cylindrical hot-wire method. A novel, 1.45 mm diameter, 50 mm long hot-wire probe was deployed. Initial measurements were made on sponge, gelatin and Styrofoam insulation to test the accuracy of the probe. Subsequent experiments conducted on sheep collagen in the range of 25 °C < T < 55 °C showed the thermal conductivity to be a linear function of temperature. Further, these changes in the thermal conductivity were found to be reversible. However, when the tissue was heated beyond 55 °C, irreversible changes in thermal conductivity were observed. Similar experiments were also conducted for determining the thermal conductivity of cow liver. In this case, the irreversible effects were found to set in much later at around 90 °C. Below this temperature, in the range of 25 °C < T < 90 °C, the thermal conductivity, as for sheep collagen, varied linearly with temperature. In the second part of our study, in vivo measurements were taken on the different organs of a living pig. Comparison with reported values for dead tissues shows the thermal conductivities of living organs to be higher, indicating thereby the dominant role played by blood perfusion in enhancing the net heat transfer in living tissues. The degree of enhancement is different in different organs and shows a direct dependence on the blood flow rate.

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).

Design of a system for contact-free measurement of the conductivity of biological tissue.

The electrical impedance of tissue can give important informations about the viability of the tissue. A non-invasive and contact-free measuring system using an inductive sensor is presented. Using a single pick-up coil the system is not sensitive enough for measuring the small changes in conductivity of biological tissue. Employing a gradiometer instead of a single pick-up coil can improve the resolution of the system. The developed data acquisition system is realized using four parts: A lock-in-amplifier, providing a sinusoidal signal and measuring the signal of the sensor, a power amplifier, driving the excitation coil of the sensor, the inductive sensor and a preamplifier for buffering a reference signal and amplifying the output signal of the sensor. In this paper the focus is on the hardware that was set up. Results of measurements on inhomogeneous phantoms are shown.

A convenient method of measuring the thermal conductivity of biological tissue

The basic principle of the thermal conductivity probe is described. Thin probes were developed based on this principle, with a reproducibility of 5.3% and relative error less than 6.0%. Each measurement can be completed in 90 s and the temperature increase can be controlled within 2 degrees C. Using the probes, the thermal conductivities of pig fat, meat, liver, kidney and live and dead snake head were measured and it was found that water content plays an important role in influencing the magnitude of the thermal conductivity of biological tissues. The probe can be used over a temperature range from -40 to 150 degrees C.

An electrodeless measuring technique for determining conductivity of biological tissues at radio frequencies

An electrodeless measuring technique for determining the conductivity of biological tissues at radio frequencies is described. The technique is based on measuring magnetic power dissipation in a conducting sample using a tuned circuit when the sample is immersed in a time-varying magnetic field. Theory regarding the measurements is presented. Consideration for coil design is given. Coil construction and measurement techniques are described in detail. The technique has three advantages: errors resulting from electrode lead inductance are completely removed; contacts between tissue surfaces and electrode surfaces are not needed; and maintaining water content and concentration of pH solution inside the tissues during measurements becomes easily facilitated. With the technique, conductivity values of dog kidney at room temperature were obtained in good agreement with previous work.

Electrical stimulation of the spinal cord: a further analysis relating to anatomical factors and tissue properties.

The midsagittal plane of the human thorax is represented by a two-dimensional finite-element model. Solutions of steady-state potential fields of bipolar epidural stimulation are computer generated. Effects of biological tissue conductivity and geometry on the fields are studied. Interpretations in terms of current density show that variations of bone conductivity have little influence on the fields. For constant current stimulation, the presence of the tough dura mater, irrespective of its thickness, does not seem to be significant. In contrast, the crucial factor affecting the field is the width of subarachnoid space which contains the highly conductive cerebrospinal fluid.

Biophysics of animal response to an electrostatic field

Numerous reports have described biological effects in animals exposed to electrostatic fields. Present equilibrium theory does not envision such effects because the bulk conductivity of biological tissue is generally held to prevent penetration of the applied electric field. Employing a two-layer mathematical model of an animal exposed to an electrostatic field we show that if the transient response of the animal is considered, then electric fields of significant strength and periodicity can occur inside the animal. We show also that the total energy available to an animal in an electrostatic field is extraordinarily small, and therefore that the biological effects associated with such exposure are not energetically driven by the applied field.

An apparatus for the measurement of the thermal conductivity of biological tissue

The thermoelectric tellurium-silver heat-flow meter disk is applied to determining the thermal conductivity of soft and moist material such as biological tissue. A disk of tissue 15 mm in diameter, 3 mm thick, is sandwiched between two meter disks in a cylindrical cup under oil. A heater at the bottom of the cup creates a current of heat through the disks; a heater winding round the periphery of the cup prevents horizontal flow of heat, being adjusted until the reading of the two heat meters is the same. Differential thermocouples measure the gradient across the specimen. The apparatus has been employed on a series of measurements of human and animal tissues.