Error analysis of tissue resistivity measurement

We identified the error sources in a system for measuring tissue resistivity at eight frequencies from 1 Hz to 1 MHz using the four-terminal method. We expressed the measured resistivity with an analytical formula containing all error terms. We conducted practical error measurements with in-vivo and bench-top experiments. We averaged errors at all frequencies for all measurements. The standard deviations of error of the quantization error of the 8-bit digital oscilloscope with voltage averaging, the nonideality of the circuit, the in-vivo motion artifact and electrical interference combined to yield an error of +/- 1.19%. The dimension error in measuring the syringe tube for measuring the reference saline resistivity added +/- 1.32% error. The estimation of the working probe constant by interpolating a set of probe constants measured in reference saline solutions added +/- 0.48% error. The difference in the current magnitudes used during the probe calibration and that during the tissue resistivity measurement caused +/- 0.14% error. Variation of the electrode spacing, alignment, and electrode surface property due to the insertion of electrodes into the tissue caused +/- 0.61% error. We combined the above errors to yield an overall standard deviation error of the measured tissue resistivity of +/- 1.96%.     

In-vivo measurement of swine myocardial resistivity

We used a four-terminal plunge probe to measure myocardial resistivity in two directions at three sites from the epicardial surface of eight open-chest pigs in-vivo at eight frequencies ranging from 1 Hz to 1 MHz. We calibrated the plunge probe to minimize the error due to stray capacitance between the measured subject and ground. We calibrated the probe in saline solutions contained in a metal cup situated near the heart that had an electrical connection to the pig's heart. The mean of the measured myocardial resistivity was 319 ohm x cm at 1 Hz down to 166 ohm x cm at 1 MHz. Statistical analysis showed the measured myocardial resistivity of two out of eight pigs was significantly different from that of other pigs. The myocardial resistivity measured with the resistivity probe oriented along and across the epicardial fiber direction was significantly different at only one out of the eight frequencies. There was no significant difference in the myocardial resistivity measured at different sites.     

Planetary exploration using a small electromagnetic sensor

A prototype broadband electromagnetic (EM) sensor, GEM-5, has been built and tested as a possible new probe for the future Mars rover to seek an ice-bonded layer at a given depth below the Martian surface. The sensor, with a vertical coaxial coil configuration, will measure the terrain resistivity and susceptibility to determine lateral variations in resistivity and magnetic susceptibility. The lateral variations will indicate regions of resistivity/susceptibility anomalies that may contain ice or water at depth. The forward solution for the sensor geometry over a layered formation and inverse algorithms to convert the EM data into the apparent susceptibility and resistivity are developed to investigate the ability of the sensor in detecting and resolving a buried (wet) ice layer in Mars-like geologic formations. Based on the simulated study, we find that the prototype sensor design should be able to resolve the lateral variations in resistivity/susceptibility under conditions of the Martian subsurface.     

A Layer Stripping Fast Algorithm for the Two-Dimensional Direct Current Inverse Resistivity Problem

The inverse problem of reconstructing the resistivity of the earth, varying both laterally and with depth, from direct current measurements is considered. The problem is formulated as a multidimensional inverse scattering problem and solved using a layer stripping algorithm. This algorithm recursively reconstructs the resistivity and electrical potential on horizontal planes of increasing depth by downward continuation. This is the first exact solution to the inverse resistivity problem for resistivity varying laterally as well as with depth. The algorithm is an extension of an algorithm proposed by Levy for resistivity varying in one dimension.     

Electrical impedance tomography using the extended Kalman filter

In this paper, we propose an algorithm that, using the extended Kalman filter, solves the inverse problem of estimating the conductivity/resistivity distribution in electrical impedance tomography (EIT). The algorithm estimates conductivity/resistivity in a wide range. The purpose of this investigation is to provide information for setting and controlling air volume and pressure delivered to patients under artificial ventilation. We show that, when the standard deviation of the measurement noise level raises up to 5% of the maximal measured voltage, the conductivity estimates converge to the expected vector within 7% accuracy of the maximal conductivity value, under numerical simulations, with spatial a priori information. A two-phase identification procedure is proposed. A cylindrical phantom with saline solution is used for experimental evaluation. An abrupt modification on the resistivity distribution of this solution is caused by the immersion of a glass object. Estimates of electrode contact impedances and images of the glass object are presented.     

Using electrical impedance to predict catheter-endocardial contact during RF cardiac ablation

During radio-frequency (RF) cardiac catheter ablation, there is little information to estimate the contact between the catheter tip electrode and endocardium because only the metal electrode shows up under fluoroscopy. We present a method that utilizes the electrical impedance between the catheter electrode and the dispersive electrode to predict the catheter tip electrode insertion depth into the endocardium. Since the resistivity of blood differs from the resistivity of the endocardium, the impedance increases as the catheter tip lodges deeper in the endocardium. In vitro measurements yielded the impedance-depth relations at 1, 10, 100, and 500 kHz. We predict the depth by spline curve interpolation using the obtained calibration curve. This impedance method gives reasonably accurate predicted depth. We also evaluated alternative methods, such as impedance difference and impedance ratio.     

非接触式随钻地层压力测试方法

地层压力是保障安全钻井的重要参数,但要想准确地获取地层压力有很大的难度.本文从数字球形聚焦电极系出发,通过与钻杆的相互结合,形成一种以电极系为探测系统的电阻率测量系统,在随钻过程中测量泥浆侵入地层的径向深度,由压力平衡原理出发,结合井筒压力和泥浆侵入深度,给出了地层压力的计算方法.上述过程的关键问题是泥浆侵入深度的测量,论文在给出总体思路的同时,研究了数字球形聚焦电极系统的相关理论和实现方法.     

外延片夹层电压数学模型推导

讨论了外延片的外延层电阻率、衬底电阻数、探针接触电阻、外延层纵向电阻与夹层电压之间的关系，推导了一种全新的二探针法测量外延夹层电压的数学公式，从而为计算外延片夹层电压提供了理论依据。     

A New Inversion Technique for Apparent Resistivity Measurements

A new algorithm for interpreting apparent earth resistivity data obtained from depth sounding measurements is presented. The method is based on fitting the data to an N layer earth model with equal layer heights h where h is equal to the required depth resolution. The spectral reflection coefficient at the earth's surface for the model used is derived as a ratio of two polynomials, the coefficients of which are a function of the resistivity ratios of adjacent layers. This provides the theoretical basis for inferring the model parameters. Measures for improving numerical stability are suggested and applied to a few examples. Results show that the present algorithm is most suited for continuously varying resistivity depth profiles.     

FEM analysis of predicting electrode-myocardium contact from RF cardiac catheter ablation system impedance

We used the finite-element method (FEM) to model and analyze the resistance between the catheter tip electrode and the dispersive electrode during radio-frequency cardiac catheter ablation for the prediction of myocardium-electrode contact. We included deformation of the myocardial surface to achieve accurate modeling. For perpendicular catheter contact, we measured the side view of myocardial deformation using X-ray projection imaging. We averaged the deformation contour from nine samples, and then incorporated the contour information into our FEM model. We measured the resistivity of the bovine myocardium using the four-electrode method, and then calculated the resistance change as the catheter penetrated into the myocardium. The FEM result of resistance versus catheter penetration depth matches well with our experimental data.     

Electrical impedance of layered atherosclerotic plaques on humanaortas

Electrical impedance measurements were performed on 13 atherosclerotic human aortic segments at 67 measuring spots in order to determine whether or not on the basis of these data a distinction can be made between atherosclerotic lesions and normal tissue. Stenosis localization and guidance of interventional techniques could be among the applications of an impedance measuring technique implemented on a catheter system. The experimental results, obtained with a two-electrode measuring technique, show that the apparent resistivity of an atherosclerotic spot does not necessarily deviate much from the resistivity of normal tissue. This is clarified by histology which shows that the majority of lesions has a surface layer of connective, fibrous tissue having almost similar conducting properties as the normal arterial wall. For gaining a deeper understanding of the way in which the measured data come about, a physical model of an atherosclerotic lesion is presented and confronted with the data. Both experimental data and theoretical considerations lead to the conclusion that only when the superficial fibrous layer is absent or very thin in relation to the size of the measuring electrode, the measured resistivity at a lesion is much higher than at normal spots. This occurs as a consequence of the high ohmic properties of the calcified or lipid deposits in the atherosclerotic lesion.     

The contact resistance at the interface between a disc electrode and an infinite slab: Mixed-boundary-value solutions

We consider the contact-resistance problem that arises when a circular-disc electrode is in imperfect contact with a semiconductor slab, the imperfect contact being modelled by an infinitely thin layer of resistive material at the interface between the disc electrode and the slab. The resulting mixed-boundary-value problem is solved through the use of basis functions that satisfy the boundary conditions outside the source region identically. Calculations of the source current-density and the total slab resistance (including the effect of the contact resistance) are performed for homogeneous slabs of different thicknesses and with different substrate resistivities, for a wide range of values of the contact resistivity of the interface layer. The results obtained show that the presence of a contact resistance tends to make the source current density distribution more uniform. They also confirm the existence of upper and lower bounds for the difference between the total slab resistance and the layer contact-resistance, as predicted by Foxhall and Lewis. Although applied only to slabs of uniform resistivity, the method can be readily extended to slabs of nonuniform resistivity.     

Characterization of fritting phenomena on Al electrode for low contact force probe card

We have investigated the characteristics of fritting of thin oxide film on an aluminum electrode for application to a probe card with low contact force. The fritting is a kind of electric breakdown of oxide film on metal electrode. It can be utilized for making electric contacts between the test probe and the electrode on LSI chips without a large force. The voltage and the contact force needed to cause fritting on a sputtered Al film was measured using W, BeCu and Pd needle probes. The contact resistance was also measured. A fritting was occurred by applying a contact load of 1 mN and voltage of 5 V. The contact resistance decreases with increasing the maximum current that passes through the contact. A current of 500 mA is enough to obtain the contact resistance of 1 /spl Omega/, which is low enough in practical test of signal lines. No damages were found on the Al film by optical microscope and scanning electron microscope observation.     

Three-dimensional electrical impedance tomography based on thecomplete electrode model

In electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. It is often assumed that the injected currents are confined to the two-dimensional (2-D) electrode plane and the reconstruction is based on 2-D assumptions. However, the currents spread out in three dimensions and, therefore, off-plane structures have significant effect on the reconstructed images. In this paper we propose a finite element-based method for the reconstruction of three-dimensional resistivity distributions. The proposed method is based on the so-called complete electrode model that takes into account the presence of the electrodes and the contact impedances. Both the forward and the inverse problems are discussed and results from static and dynamic (difference) reconstructions with real measurement data are given. It is shown that in phantom experiments with accurate finite element computations it is possible to obtain static images that are comparable with difference images that are reconstructed from the same object with the empty (saline filled) tank as a reference.     

Construction and validation of a plunge electrode array for three-dimensional determination of conductivity in the heart.

The heart's response to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. Analysis of the microstructure of the heart predicts that three unique intracellular electrical conductances can be defined at any point in the ventricular wall; however, to date, there has been no experimental confirmation of this concept. We report the design, fabrication, and validation of a novel plunge electrode array capable of addressing this issue. A new technique involving nylon coating of 24G hypodermic needles is performed to achieve nonconductive electrodes that can be combined to give moderate-density multisite intramural measurement of extracellular potential in the heart. Each needle houses 13 silver wires within a total diameter of 0.7 mm, and the combined electrode array gives 137 sites of recording. The ability of the electrode array to accurately assess conductances is validated by mapping the potential field induced by a point current source within baths of saline of varying concentration. A bidomain model of current injection in the heart is then used to test an approximate relationship between the monodomain conductivities measured by the array, and the full set of bidomain conductivities that describe cardiac tissue.     

The effect of plunge electrodes during electrical stimulation of cardiac tissue

The mechanism for far-field stimulation of cardiac tissue is not known, although many hypotheses have been suggested. This paper explores a new hypothesis: the insulated plunge electrodes used in experiments to map the extracellular potential may affect the transmembrane potential when an electric field is applied to cardiac tissue. Our calculation simulates a 10-mm-diameter sheet of passive tissue with a circular insulated plunge electrode in the middle of it, ranging in diameter from 0.05 to 2 mm. We calculate the transmembrane potential induced by a 500-V/m electric field. Our results show that a transmembrane potential is induced around the electrode in alternating areas of depolarization and hyperpolarization. If the electric field is oriented parallel to the myocardial fibers, the maximum transmembrane potential is 89 mV. A layer of fluid around the electrode increases the transmembrane potential. We conclude that plunge electrodes may introduce artifacts during experiments designed to study the response of the heart to strong electric shocks.     

Lateral SbTeN based multi-layer phase change memory for multi-state storage

X-ray diffraction patterns and resistivity measurement indicate that as-deposited N-doped Sb₂Te₃ (STN) films become amorphous while the as-deposited Sb₂Te₃ film is crystalline. A lateral as-deposited STN-based multi-layer phase change memory was proposed for multi-state storage. The active region of the device consists of a top 30-nm TiN/180-nm STN/20-nm TiN/bottom 120-nm STN stacked multi-layer. Static switching properties of the device with STN initially starting from the amorphous state exhibit two apparent S-shaped switchings, which correspond to two marked device resistance drops by a factor of 2-5. The first and second threshold voltages are around 2.8-3.2 and 4.3-5.4 V, respectively. Finite element analysis of the device shows that the two switchings could sequentially occur at the electrode steps from the bottom 120-nm STN layer to the top thick 180-nm STN layer.     

Resistivity measurement of thin doped semiconductor layers by means of four point-contacts arbitrarily spaced on a circumference of arbitrary radius

The resistivity of a thin doped semiconductor layer or wafer measured in the vicinity of four point contacts placed on the semiconductor surface is shown to be independent of the relative distance between the contacts, provided the contacts are located on a circumference, and the distance to the boundary of the surface will not fall short of the greatest actual spacing between contacts. This method combines the advantage of the four probe resistivity measurement originally proposed by Valdés, that is the determination of ρ in a restricted layer region, with the advantage of arbitrary spacing of the probes, which characterizes van der Pauw's method. Experiments are in agreement with results obtained by the measuring methods of Valdés and van der Pauw.     

Multisite microprobes for neural recordings

Multisite, passive microprobes have been developed to allow simultaneous recording of action potential activity from multiple neurons at different locations in the brain. The microprobes were fabricated using standard integrated circuit techniques. The probe is a planar structure that consists of gold electrodes sandwiched between two polyimide dielectric layers and bonded to a molybdenum structural support. Windows in the top dielectric layer expose the electrode sites and bonding pads. In two distinct versions of the probe four or six recordings sites, respectively, of approximately 25 microns 2 are arranged on a dagger-shaped structure which can penetrate the pia. The bonding pads and interconnect wires at the probe head are entirely encapsulated in a tubular fixture that is packed with silicone RTV and sealed with epoxy to protect the interconnections from contact with body fluids. The site impedances at 1 kHz are typically between 2 and 4 M omega. Probe lifetimes for continuous immersion in physiological saline solution, as measured by impedance, have exceeded 750 h. The failure mechanism is believed to be due to moisture and ion absorption in the top dielectric layer. In acute neurophysiological experiments using the four site probes, action potential activity was recorded from physiologically identified neurons in the dorsal column nuclei of anesthetized rat.     

硅片少子寿命的直排四探针测试

用直排四探针方法测试硅抛光片的电阻率时 ,减少表面复合和增大测试电流故意引进注入使电阻率减少 ,根据电导率与少数载流子寿命成正指数增加的关系 ,求得少子寿命