Minimum Number Of Electrodes Research Articles

A Spectrotemporal EEG Mapping Approach for Decoding Imagined Marathi Language Phonemes

Individuals facing verbal communication impairments resulting from brain disorders like paralysis or autism encounter significant challenges when unable to articulate speech. This research proposes the design and development of a wearable system capable of decoding imagined speech using electroencephalogram (EEG) signals obtained during the mental process of speech generation. The system’s main objective is to offer an alternative communication method for individuals who can hear and think but face challenges in articulating their thoughts verbally. The design suggested includes user-friendliness, wearability, and comfort for seamless integration into daily life. A minimal number of electrodes are strategically placed on the scalp to minimize invasiveness. Achieving precise localization of the cortical areas responsible for generating the EEG patterns during imagined speech is vital for accurate decoding. Literature studies are utilized to determine the cortical positions associated with speech processing. Due to the inherent limitations in EEG spatial resolution, meticulous experiments are conducted to map the scalp positions onto their corresponding cortical counterparts. Specifically, we focus on identifying the scalp location over the superior temporal gyrus (T3) using the internationally recognized 10-20 electrode placement system by employing a circular periphery movement with a 2 cm distance increment. Our research involves nine subjects spanning various age groups, with the youngest being 23 and the oldest 65. Each participant undergoes ten iterations, during which they imagine six Marathi syllables. Our work contributes to the development of wearable assistive technology, enabling mute individuals to communicate effectively by translating their imagined speech into actionable commands. This innovation ultimately enhances their social participation and overall well-being.

Improved Configurations for 3D Acoustoelectric Tomography With a Minimal Number of Electrodes.

Acoustoelectric tomography (AET) is a hybrid imaging technique combining ultrasound and electrical impedance tomography (EIT). It exploits the acoustoelectric effect (AAE): an US wave propagating through the medium induces a local change in conductivity, depending on the acoustoelectric properties of the medium. Typically, AET image reconstruction is limited to 2D and most cases employ a large number of surface electrodes. This article investigates the detectability of contrasts in AET. We characterize the AEE signal as a function of the medium conductivity and electrode placement, using a novel 3D analytical model of the AET forward problem. The proposed model is compared to a finite element method simulation. In a cylindrical geometry with an inclusion contrast of 5 times the background and two pairs of electrodes, the maximum, minimum, and mean suppression of the AEE signal are 68.5%, 3.12%, and 49.0%, respectively, over a random scan of electrode positions. The proposed model is compared to a finite element method simulation and the minimum mesh sizes required successfully model the signal is estimated. We show that the coupling of AAE and EIT leads to a suppressed signal and the magnitude of the reduction is a function of geometry of the medium, contrast and electrode locations. This model can aid in the reconstruction of AET images involving a minimum number of electrodes to determine the optimal electrode placement.

Mild cognitive impairment detection with optimally selected EEG channels based on variational mode decomposition and supervised machine learning

Detecting mild cognitive impairment (MCI), which is typically the earliest stage of dementia, is essential for managing dementia. Recently, researchers have explored the use of electroencephalography (EEG) to detect MCI. EEG involves recording brain activity by placing a number of electrodes (channels) directly on the scalp. Here we present effective variational mode decomposition (VMD)-based methods for detection of MCI with optimally selected EEG channels. To achieve this, we first decompose the EEG signals from each channel into sub-signals called variational mode functions (VMFs) with different frequency bands. From each VMF, an entropy measure is used to extract a feature. Several supervised machine learning techniques are investigated to classify the resulting features and obtain full-channel classification accuracy. We assess the classification performance of the proposed methods on 19-channel EEGs recorded from 32 healthy subjects and 29 MCI patients in the resting state. In a second step, we explore the feasibility of reducing the number of EEG channels while maintaining classification accuracy by using several EEG channel selection methods. Specifically, we study the effectiveness of non-dominated sorting genetic algorithm (NSGA)-based methods (multi-objective optimization methods), in addition to greedy algorithms such as back-elimination and forward-addition. Results show that selecting a few suitable channels can lead to similar or even superior accuracy compared to a classifier that utilizes all EEG channels. The results also show that the multi-objective NSGA optimization methods have a greater ability than the greedy methods to select few compatible channels. For example, 99.51% is the maximum accuracy achieved using all 19 EEG channels when processed with a combination of VMD, log energy entropy, and a K-nearest neighbor (KNN) classifier. The same accuracy is achieved with only 9 channels selected by NSGA, compared to 13 channels for greedy algorithms. With an ensemble KNN classifier, the highest accuracy, 99.81%, is achieved using 11 channels selected by an NSGA-based method. The results are encouraging, demonstrating that this brain disorder can be accurately diagnosed using a minimal number of electrodes and paving the way for its adoption in clinical practice.

Identification of Alzheimer’s disease from central lobe EEG signals utilizing machine learning and residual neural network

Cognitive and behavioral deficits are some of the symptoms of Alzheimer's disease, a neurological disease caused by brain deterioration. Early diagnosis of the disease minimizes the disease's progression. In this way, patients' living standards can be maintained. An experienced specialist will assess the results of grueling diagnostic tests and a costly diagnosis process.This motivation led to the creation of a fully automated computer system, which uses the proposed methods to detect Alzheimer's disease from EEG signals acquired from a minimum number of electrodes: three central lobe electrodes. This work presents the advantages of implementing the proposed system. Two different datasets were presented to evaluate the system’s performance. After preprocessing the raw EEG data, wavelet transforms were applied to calculate statistical properties. First, the paper discusses the performance of different traditional machine learning classifiers: Diagonal Discriminant Analysis, Support Vector Machine (LSVM, RBF), K-Nearest Neighbors, Random Forest, Logistic Regression, and Naïve Bayes. By comparing the classifiers’ performance, it is found that Naïve Bayes and LSVM classifiers yield the highest performance of 96.55% and 95.69% when applied to the first dataset and 96.55% and 94.52% for the second dataset, respectively. “ResNet-50” Convolutional Neural Network classifier was implemented to demonstrate the capability of constructing an effective AD diagnosing system. It yields an accuracy of 97.8261% when applied to the first dataset.This work shows how Deep Learning improves the performance of classification in early medical diagnosis, which will enhance different diseases’ treatment, as “Resnet – 50” convolutional neural network classifier outperformed Naïve Bayes Classifier.

Structural health monitoring of CFRPs using electrical resistance by reduced peripheral electrodes

In this study, structural health monitoring (SHM) methods of carbon fiber reinforced plastics (CFRPs) were investigated using electrical resistance. The developed sensing technique monitored electrical resistance in accordance with the impact damage of a CFRP. The changes in electrical resistances with multiple electrode sets enabled SHM without extra sensors so that this technique can be called self-sensing. Moreover, this study proposed electrodes only at peripheral side of a structure to minimize the number of electrodes compared to those in an array which has square number of sensors as the sensing area increases. For the intensive investigation, electromechanical sensitivity in terms of electrode distance was analyzed and optimized under drop weight impact testing. Then, SHM methods with electrodes in an array and electrodes in peripheral edges were comparatively investigated. The developed methods successfully localized impact damages into 2D coordinates. Furthermore, damage severity can be shown with a damage map by calculating electrical resistance change ratio. Therefore, structural health self-sensing system using electrical resistance was successfully developed with the minimum number of electrodes.

Catheter ablation of the cavotricuspid isthmus in patients with atrial flutter: predictors of long-term outcomes.

Predictors of long‑term outcomes and an optimal catheter set for ablation of the cavotricuspid isthmus in patients with atrial flutter (AFL) are not well known. This study aimed to identify predictors of clinical events following ablation. We studied 741 patients (mean [SD] age, 62.2 [10.8] years; 248 women) who were followed for a mean (SD) time of 4.4 (2.7) years. The 2- versus 3‑electrode approach and clinical predictors ofclinical events during follow‑up were analyzed. The 2‑electrode approach was faster (mean [SD] time, 62.5 [30.3] vs 101.4 [51] min; P <0.001), associated with shorter fluoroscopy time (13.1 [9.3] vs 20.3 [12.4] min; P < 0.001), cost‑effective (8.29 [2.82] vs 11.89 [2.51] units; P <0.001), and more effective (92.1% vs 86.1%; P = 0.012). The independent predictors of AFL recurrence were: calcium blocker use (hazard ratio [HR], 3.24; 95% CI, 1.64-6.4), mitral valve disease (HR, 1.82; 95% CI, 1.12-2.95), previous stroke and/ or TIA (HR, 2.38; 95% CI, 1.21-4.65), pulmonary artery dilatation (HR, 3.94; 95% CI, 1.22-12.73), and previous pulmonary embolism (HR, 3.77; 95% CI, 1.14-12.43); of atrial fibrillation (AF): previous AF (HR, 6.054; 95% CI, 4.58-8), left atrial enlargement (HR, 1.43; 95% CI, 1.12-1.81), number of antiarrhythmic drugs used (HR, 1.16; 95% CI, 1.05-1.28), and mitral valve disease (HR, 1.28; 95% CI, 1.04-1.58); of pacemaker implantation: tachycardia‑bradycardia syndrome (HR, 6.17; 95% CI, 3.16-12.05), previous second-/third‑degree atrioventricular block (HR, 29.4; 95% CI, 7.37-117.28), centrally acting hypotensive drugs (HR, 29.55; 95% CI, 6.14-142.25), aortic dilatation or aneurysm (HR, 2.58; 95% CI, 1.06-6.3), a labile international normalized ratio (HR, 3.45; 95% CI, 1.72-6.93), left bundle branch block (HR, 4.7; 95% CI, 1.49-14.82), the shortest R‑R interval during AFL (HR, 1.003; 95% CI, 1.001-1.005), previous cardiac surgery (HR, 2.69; 95% CI, 1.27-5.7), and aortic valve disease (HR, 2.22; 95% CI, 1.08-4.59). Ablation of cavotricuspid isthmus with a minimal number of electrodes is safe and effective. Specific predictors of clinical events during long‑term follow-up can be determined.

P955Non-invasive mapping: what is the minimal number of electrodes needed to obtain a good spatial resolution of the activation map?

Abstract Introduction and aims The 12-lead ECG is highly inaccurate for localization of the site of origin of supraventricular and ventricular arrhythmias. Non-invasive mapping systems (ECGI) based on a high number of electrodes recording the electrical activity on the surface of the torso have already proven good accuracy for mapping different arrhythmic substrates. The aim of this study was to assess what is the minimal number of leads needed to obtain a precise mapping with the ECGI. Methods This study enrolled 14 patients (9 male, median age 50 (44-58) years) referred to our center for catheter ablation of premature ventricular contractions (PVC). Patients underwent pre-procedural ECGI using the epicardial and endocardial mapping system . This system uses the DICOM images from contrast computed tomography of the heart and up to 28 adhesive electrodes with 8 leads each, adding up to 224 body-surface leads. All patients underwent invasive electroanatomical mapping and ablation with the magnetic navigation system. We analysed the number of recording leads used to construct the non-invasive activation map of the PVCs and the accuracy and the spatial resolution of the map when comparing to the invasive map. We then reprocessed the exam, using progressively less leads until we only left the leads placed in the standard 12 lead ECG positions and evaluated the concordance with the invasive map as well as the spatial resolution. We considered an earliest activation site (EAS) area of 1 cm2 a good spatial resolution and using a ROC curve we calculated the minimal number of leads necessary to obtain a good spatial resolution. Results The median number of electrodes used for the initial map was 170 (138-177). Concordance between non-invasive and invasive site of origin occurred in 11 out of 14 patients. The results are presented in the Table. The minimal number of electrodes to have a good spatial resolution was 100. The area of EAS was significantly lower when using more than 100 leads, respectively 0.65 (0.5-1) cm2 versus 3 (1.6-5) cm2, p &amp;lt; 0.001. Conclusions The minimal number of leads to achieve a good spatial resolution was high. Reducing the number of leads resulted in a significant decrease in spatial resolution and a lower concordance rate. ECGI data Number of adhesive electrodes Median number of leads Amycard/Carto concordance Median area of EAS in the ECGI (cm2) Maximal nº electrodes 170 (138-177) 11/14 0.64 (0.5-0.9) 12 electrodes 76 (61-80) 11/14 1.6 (1.4-2.6) 6 electrodes (2 Ant, 2 Lat ,2 Post) 38 (32-44) 9/14 4.3 (3.2-5.4) 12 leads 12 0/14 - Ant anterior; Lat: lateral; Post: posterior; EAS: early activation site. Abstract Figure. Area of EAS according to the N of leads

Two degrees of freedom, dynamic, hand-wrist EMG-force using a minimum number of electrodes

Few studies have related the surface electromyogram (EMG) of forearm muscles to two degree of freedom (DoF) hand-wrist forces; ones that have, used large high-density electrode arrays that are impractical for most applied biomechanics research. Hence, we researched EMG-force in two DoFs—hand open-close paired with one wrist DoF—using as few as four conventional electrodes, comparing equidistant placement about the forearm to optimized site selection. Nine subjects produced 1-DoF and 2-DoF uniformly distributed random forces (bandlimited to 0.75 Hz) up to 30% maximum voluntary contraction (MVC). EMG standard deviation (EMGσ) was related to force offline using linear dynamic regression models. For 1-DoF forces, average RMS errors using two optimally-sited electrodes ranged from 8.3 to 9.0 %MVC, depending on the DoF. For 2-DoFs, overall performance was best when training from both 1- and 2-DoF trials, giving average RMS errors using four optimally-sited electrodes of 9.2 %MVC for each DoF pair (hand open-close paired with one wrist DoF). For each model, additional optimally-sited electrodes showed little statistical improvement. Electrodes placed equidistant performed noticeably poorer than an equal number of electrodes that were optimally sited. The results suggest that reliable 2-DoF hand-wrist EMG-force with a small number of electrodes may be feasible.

Simultaneous Recording of ICG and ECG Using Z-RPI Device with Minimum Number of Electrodes

Impedance cardiography (ICG) is a noninvasive method for monitoring mechanical function of the heart with the use of electrical bioimpedance measurements. This paper presents the feasibility of recording an ICG signal simultaneously with electrocardiogram signal (ECG) using the same electrodes for both measurements, for a total of five electrodes rather than eight electrodes. The device used is the Z-RPI. The results present good performance and show waveforms presenting high similarity with the different signals reported using different electrodes for acquisition; the heart rate values were calculated and they present accurate evaluation between the ECG and ICG heart rates. The hemodynamics and cardiac parameter results present similitude with the physiological parameters for healthy people reported in the literature. The possibility of reducing number of electrodes used for ICG measurement is an encouraging step to enabling wearable and personal health monitoring solutions.

Computational Feasibility Analysis of Electrochemotherapy With Novel Needle-Electrode Arrays for the Treatment of Invasive Breast Ductal Carcinoma.

Breast cancer represents a rising problem concerning public health worldwide. Current efforts are aimed to the development of new minimally invasive and conservative treatment procedures for this disease. A treatment approach for invasive breast ductal carcinoma could be based on electroporation. Hence, in order to determine the effectiveness of electrochemotherapy in the treatment of this disease, 12 electrode models were investigated on realistic patient-specific computational breast models of 3 patients diagnosed by Digital Breast Tomosynthesis imaging. The electrode models exhibit 4, 5, and 6 needles arranged in 4 geometric configurations (delta, diamond, and star) and 3 different needle spacing resulting in a total of 12 needle-electrode arrays. Electric field distribution in the tumors and a surrounding safety margin of 1 cm around the tumor edge is computed using the finite element method. Efficiency of the electrode arrays was determined hierarchically based on (1) percentage of tumor volume reversibly electroporated, (2) percentage of tumor volume irreversibly electroporated, (3) percentage of treated safety margin volume, (4) minimal invasiveness, that is, minimal number of electrodes used, (5) minimal activated electrode pairs, and (6) minimal electric current. Results show that 3 electrode arrays (4 needle-delta, 5 needle-diamond, and 6 needle-star) with fixed-geometry configuration could be used in the treatment with electrochemotherapy of invasive breast ductal carcinomas ranging from 1 to 5 cm3 along with a surrounding safety margin of 1 cm.

Two degrees of freedom quasi-static EMG-force at the wrist using a minimum number of electrodes

Surface electromyogram-controlled powered hand/wrist prostheses return partial upper-limb function to limb-absent persons. Typically, one degree of freedom (DoF) is controlled at a time, with mode switching between DoFs. Recent research has explored using large-channel EMG systems to provide simultaneous, independent and proportional (SIP) control of two joints—but such systems are not practical in current commercial prostheses. Thus, we investigated site selection of a minimum number of conventional EMG electrodes in an EMG-force task, targeting four sites for a two DoF controller. In a laboratory experiment with 10 able-bodied subjects and three limb-absent subjects, 16 electrodes were placed about the proximal forearm. Subjects produced 1-DoF and 2-DoF slowly force-varying contractions up to 30% maximum voluntary contraction (MVC). EMG standard deviation was related to forces via regularized regression. Backward stepwise selection was used to retain those progressively fewer electrodes that exhibited minimum error. For 1-DoF models using two retained electrodes (which mimics the current state of the art), subjects had average RMS errors of (depending on the DoF): 7.1–9.5% MVC for able-bodied and 13.7–17.1% MVC for limb-absent subjects. For 2-DoF models, subjects using four electrodes had errors on 1-DoF trials of 6.7–8.5% MVC for able-bodied and 11.9–14.0% MVC for limb-absent; and errors on 2-DoF trials of 9.9–11.2% MVC for able-bodied and 15.8–16.7% MVC for limb-absent subjects. For each model, retaining more electrodes did not statistically improve performance. The able-bodied results suggest that backward selection is a viable method for minimum error selection of as few as four electrode sites for these EMG-force tasks. Performance evaluation in a prosthesis control task is a necessary and logical next step for this site selection method.

Time-frequency optimization for discrimination between imagination of right and left hand movements based on two bipolar electroencephalography channels

AbstractTo enforce a widespread use of efficient and easy to use brain-computer interfaces (BCIs), the inter-subject robustness should be increased and the number of electrodes should be reduced. These two key issues are addressed in this contribution, proposing a novel method to identify subject-specific time-frequency characteristics with a minimal number of electrodes. In this method, two alternative criteria, time-frequency discrimination factor (TFDF) andFscore, are proposed to evaluate the discriminative power of time-frequency regions. Distinct from classical measures (e.g., Fisher criterion,r2coefficient), the TFDF is based on the neurophysiologic phenomena, on which the motor imagery BCI paradigm relies, rather than only from statistics.Fscore is based on the popularFisher’sdiscriminant and purely data driven; however, it differs from traditional measures since it provides a simple and effective measure for quantifying the discriminative power of a multi-dimensional feature vector. The proposed method is tested on BCI competition IV datasets IIa and IIb for discriminating right and left hand motor imagery. Compared to state-of-the-art methods, our method based on both criteria led to comparable or even better classification results, while using fewer electrodes (i.e., only two bipolar channels, C3 and C4). This work indicates that time-frequency optimization can not only improve the classification performance but also contribute to reducing the number of electrodes required in motor imagery BCIs.

Influence of Electrode Placement on Signal Quality for Ambulatory Pregnancy Monitoring

Noninvasive fetal health monitoring during pregnancy has become increasingly important in order to prevent complications, such as fetal hypoxia and preterm labor. With recent advances in signal processing technology using abdominal electrocardiogram (ECG) recordings, ambulatory fetal monitoring throughout pregnancy is now an important step closer to becoming feasible. The large number of electrodes required in current noise-robust solutions, however, leads to high power consumption and reduced patient comfort. In this paper, requirements for reliable fetal monitoring using a minimal number of electrodes are determined based on simulations and measurement results. To this end, a dipole-based model is proposed to simulate different electrode positions based on standard recordings. Results show a significant influence of bipolar lead orientation on maternal and fetal ECG measurement quality, as well as a significant influence of interelectrode distance for all signals of interest.

The recognition of multi-finger prehensile postures using LDA

The prehensile hand gestures play an important role in daily living for seizing or holding subjects stably. In order to realize the accurate recognition of eight prehensile hand gestures with a minimal number of electrodes, an off-line myoelectric control system with only two electrodes is developed. We choose Mean Absolute Value, Variance, the fourth-order Autoregressive Coefficient, Zero Crossings, Mean Frequency and Middle Frequency as original electromyography feature set and utilize the linear discriminant analysis to reduce the dimension and complete classification. The extent of dimension reduction is investigated and on the premise of it, the average accuracy can achieve 97.46% in the recognition of six hand gestures. The optimal feature set based on the original feature set is determined to be Mean Absolute Value, Variance, and the fourth-order Autoregressive Coefficient, which yields an average accuracy of 95.94% in the recognition of eight hand gestures. An average method is proposed to improve the accuracy further, resulting in the average accuracy in eight gestures being 98.12% and the best individual accuracy of some hand gestures being 100%.

Double-Cross Hydrostatic Pressure Sample Injection for Chip CE: Variable Sample Plug Volume and Minimum Number of Electrodes

A novel sample injection method for chip CE was presented. This injection method uses hydrostatic pressure, generated by emptying the sample waste reservoir, for sample loading and electrokinetic force for dispensing. The injection was performed on a double-cross microchip. One cross, created by the sample and separation channels, is used for formation of a sample plug. Another cross, formed by the sample and controlling channels, is used for plug control. By varying the electric field in the controlling channel, the sample plug volume can be linearly adjusted. Hydrostatic pressure takes advantage of its ease of generation on a microfluidic chip, without any electrode or external pressure pump, thus allowing a sample injection with a minimum number of electrodes. The potential of this injection method was demonstrated by a four-separation-channel chip CE system. In this system, parallel sample separation can be achieved with only two electrodes, which is otherwise impossible with conventional injection methods. Hydrostatic pressure maintains the sample composition during the sample loading, allowing the injection to be free of injection bias.

Theory of simultaneous control of orientation and translational motion of nanorods using positive dielectrophoretic forces

The manipulation of individual submicron-sized objects has been the focus of significant efforts over the last few years. A method to arbitrarily move and orient a set of rod-shaped conductive particles in a region defined by a set of electrodes using positive dielectrophoretic forces is presented. While the orientation of each particle is directly specified through the angle of the local electric field, its position is indirectly controlled through the applied force. Each electrode is approximated as an unknown point charge and an induced dipole. Since each induced dipole results from the combination of all other sources, a set of linear constraints are derived to enforce the self-consistency of the system. Additionally, the force and orientation of each particle also form an additional set of linear constraints. This combined set of constraints is then solved numerically to yield the sources required to induce the desired orientation and motion of each particle. It is observed that the minimum number of electrodes that can be used to control a set of N particles is 4N+1. Numerical simulations demonstrate that the control of a single nanorod (diameter of 70nm; length of 1.4μm) in the midst of a realistic electrode array can be accomplished under practical conditions. In addition, such control of orientation and motion can be achieved over an ample region in the vicinity of each rod.

Glass Conductance Controlled Electric Forehearth

The heating currents flow longitudinally between transverse submerged electrodes. Their arrangement distributes heating current throughout the glass body without zone control interference while using a minimum number of electrodes. Conventional gas firing remains unchanged as an alternate mode of operation. Heating is controlled to an average glass electric conductance setting (as measured in the exit half of each zone). The basic electrode and holder design is briefly described. It does not require forced cooling. The operator's control panel is explained in addition to the all solid-state measuring, calculating, and controlling system with glass level compensation. A muffled cooling system improvement is also outlined.

Physical Scale Modelling of Electrothermic Thawing of Permafrost For Alleviation of Frost Heave Problems In Chilled Gas Pipelines

Abstract The artificial thawing of permafrost beneath chilled gas pipelines by electrical current flawing through the frozen medium Is studied by means of scaled physical models. Techniques are described whereby, by use of a minimal number of electrodes embedded in the frozen medium, extended zones can be thawed beneath the pipeline so that the pipe can settle and frost heave stresses can be relieved. INTRODUCTION The design and construction of pipelines in cold regions entail special problems. It is well known, for instance, that pipelines passing through zones of continuous and discontinuous permafrost may cause ground slumping or frost heaving if adequate design measures are not taken. As an example, over half the length of the 1.22-m-diameter Alyeska oil pipeline has had to be elevated on special piles to prevent the warm oil from thawing the underlying ground ice, which in turn would have caused unacceptable subsidence of the pipe. Plans for the ill-fated 1.22-m-diameter Mackenzie Valley gas pipeline called for chilling the gas so that the cold pipe could be buried and not cause thawing of permafrost and ground ice. It was evident, however, that in zones of discontinuous permafrost, freezing of the soil around the chilled pipe would, over a period of years, cause frost heave and attendant unacceptable differential stresses in the pipeline. The route of the recently approved Alcan gas pipeline presents geotechnical problems -that are similar to those of the Mackenzie Valley route. It is again deemed advisable to bury the pipeline and to chill the gas in order to avoid ground thawing and subsidence. As before, this leads to problems in zones of discontinuous permafrost due to soil freezing and frost heave. Various proposals have been advanced for overcoming the frost heave problem. Initially, it was thought that an earth berm placed above the pipeline would weight down the pipe to counter eventual frost heave pressures. It now seems, however, that frost heave pressures are too great to be controlled in this fashion. Other approaches that have been suggested include fishing. Construction of the packer element is very similar to a high-pressure hydraulic hose with steel braided carcass layers. Unlike a hydraulic hose, the packer expands as required when internal pressure is applied. Expansion is allowed by special braid angles in the packer carcass. Like a hydraulic hose, the packer element also has metal collars on both ends. The collars anchor both ends of the steel braid cables, and are threaded to fit the packer assembly. Limitations of the Equipment Inflatable packer equipment is limited mainly by the differential pressure holding ability of the packer elements. However, this is affected to a large extent by the diameter that the packer element has been inflated to. With the hole in good condition and close to gauge, the packer elements have had no trouble holding differential pressures in excess of 30,000 kPa. However, because one of the main uses of inflatable packer equipment is in washed-out holes.

Mathematical analysis of body surface potentials

Summary It has been shown that the dipole moment of the heart can be found from integrations of body surface potentials. For a given horizontal level and at a fixed instant of time during the QRS complex the variation of potentials along the periphery of the body can be expressed mathematically by polynomial functions. Knowledge of the degree, i.e. the highest power of the polynomial, can be of great advantage, because there are mathematical relationships between the degree of the polynomial and the number of sampling sites necessary to obtain accurate integration results. In the present study, body surface potentials were obtained from two humans, one dog and two monkeys. The potentials of the QRS period were digitized at 5 or 10 equidistant time intervals and analyzed into x- and z-components and were expressed in terms of polynomials, one polynomial per horizontal level per instant within the cardiac cycle. The highest observed polynomial degree was 7. Then the polynomials were integrated around the periphery of every horizontal level and the values of the integrals were expressed as functions of their position along the longitudinal axis of the body. New polynomials were fitted on the new functions with a highest observed degree of 5. These results will be helpful in designing vector lead systems giving a maximal accuracy with a minimal number of electrodes.