Effects of the torso boundary and internal conductivity interfaces in electrocardiography: An evaluation of the ‘Infinite medium’ approximation

The analytic, eccentric spheres model of the torso was used to examine the validity of approximating the ‘infinite medium’ potential by integrating ‘finite medium potentials’ over the torso surface. Although idealized, the analytic model is sophisticated enough for all important torso conductivity and geometry parameters to be preserved in the formulation. The model generates both ‘finite medium’ potentials (for which the torso is surrounded by air) and also ‘infinite medium’ potentials (for which the outermost layer of the torso extends outward to infinity). The finite medium torso potentials were integrated over the torso surface in accordance with the approximation used by many investigators in an effort to make the surface distribution more representative of the primary cardiac sources. The resulting potential distribution was compared with the true infinite medium potential, in which the effects of internal inhomogeneities (secondary sources) were taken into account. The difference between the two representations was found to be significant, and caution should be used when interpreting such data.     

Cellular membrane potentials induced by alternating fields

Membrane potentials induced by external alternating fields are usually derived assuming that the membrane is insulating, that the cell has no surface conductance, and that the potentials are everywhere solutions of the Laplace equation. This traditional approach is reexamined taking into account membrane conductance, surface admittance, and space charge effects. We find that whenever the conductivity of the medium outside the cell is low, large corrections are needed. Thus, in most of the cases where cells are manipulated by external fields (pore formation, cell fusion, cell rotation, dielectrophoresis) the field applied to the cell membrane is significantly reduced, sometimes practically abolished. This could have a strong bearing on present theories of pore formation, and of the influence of weak electric fields on membranes.     

Comparison and testing of least-squares time domain inverse solutions in electrocardiography

The use of several mathematical methods for estimating epicardial ECG potentials from arrays of body surface potentials has been reported in the literature; most of these methods are based on least-squares reconstruction principles and operate in the time-space domain. In this paper we introduce a general Bayesian maximum a posteriori (MAP) framework for time domain inverse solutions in the presence of noise. The two most popular previously applied least-squares methods, constrained (regularized) least-squares and low-rank approximation through the singular value decomposition, are placed in this framework, each of them requiring the a priori knowledge of a ‘regularization parameter’, which defines the degree of smoothing to be applied to the inversion. Results of simulations using these two methods are presented; they compare the ability of each method to reconstruct epicardial potentials. We used the geometric configuration of the torso and internal organs of an individual subject as reconstructed from CT scans. The accuracy of each method at each epicardial location was tested as a function of measurement noise, the size and shape of the subarray of torso sensors, and the regularization parameter. We paid particular attention to an assessment of the potential of these methods for clinical use by testing the effect of using compact, small-size subarrays of torso potentials while maintaining a high degree of resolution on the epicardium.     

人体躯干模型中肺的存在对体表电位分布的影响

在所建三维人体躯干模型的基础上,给出了如何应用边界元方法对非均匀人体场域进行求解。在设定心外膜电位分别呈现为单偶极子和双偶极子时,求出相应非均匀场域中的体表电位分布,并将它们与相同情况下均匀场域的体表电位分布进行分析比较。结果表明：躯干模型中肺的存在虽然对体表电位中极值的大小和位置没有太大影响,但却较大程序地改变了整个体表电位的分布状况,具体地说,就是由于肺的存在使得体表电位值较均匀时的相对误差高     

改善心电图逆问题病态条件的两个有效方法

本文对应用数值方法求解三维心电图逆问题时出现的解的不稳定现象,提出了两种有效的解决办法,即提高电导率值和选用包含适当的正则因子的阻尼最小二乘法。文中应用有限元和边界元结合的方法,在一个包含各向异性导电性肌肉层的三维人体模型下进行了心外膜电位的重构计算。其结果证明这种方法对提高心电图逆问题的数值稳定性和解的精度非常有效。     

Approach for an equation of state for adsorbed protein surfaces.

A surface equation of state for polymer interfaces is obtained by equating the chemical potentials of the solvent in the bulk and surface phases. This equation of state contains the fraction of the surface covered with polymer and the surface activity coefficient as parameters. These parameters may be obtained by measuring the thermodynamic modulus of elasticity. Moreover, if the amount of protein in the interface is known the degree of folding in the surface may be evaluated. The present theory was applied to adsorbed beta-lactoglobulin in surfaces. The results are in agreement with qualitative equations and results from other sources.     

The effect of the torso boundary in electrocardiography

This paper outlines and contrasts three different (external) “infinite medium” potential fields which may be obtained (in principle) from known geometry, conductivities, and bounded medium torso potentials. Their electrocardiographic implications are considered.     

Surface charge, surface dipoles and membrane conductance

The conductance of lipid membranes in the presence of nonactin is changed by the adsorption of small amounts of ionic and zwitterionic surfactants. The conductance changes are, in many instances, not accounted for by the variation in surface charge or diffuse double layer potential as calculated from Gouy-Chapman theory. The changes are, however, all accurately accounted for by the variation in total potential across the membrane interface. This potential includes contributions from surface dipoles and specific adsorption, as well as any diffuse double layer effects not included in the Gouy-Chapman theory.The total potential changes were inferred from Volta or compensational potential changes at bulk oil (and monolayer)/aqueous solution interfaces. Surface charge densities were found by standard thermodynamic methods involving the use of the Gibbs equation. Electrokinetic potentials for the appropriate surfaces were also measured and, in general, agreed well with the diffuse double layer potentials calculated from the Gouy-Chapman theory.     

Computational issues of importance to the inverse recovery of epicardial potentials in a realistic heart-torso geometry

In vitro data from a realistic-geometry electrolytic tank were used to demonstrate the consequences of computational issues critical to the ill-posed inverse problem in electrocardiography. The boundary element method was used to discretize the relationship between the body surface potentials and epicardial cage potentials. Variants of Tikhonov regularization were used to stabilize the inversion of the body surface potentials in order to reconstruct the epicardial surface potentials. The computational issues investigated were (1) computation of the regularization parameter; (2) effects of inaccuracy in locating the position of the heart; and (3) incorporation of a priori information on the properties of epicardial potentials into the regularization methodology. Two methods were suggested by which a priori information could be incorporated into the regularization formulation: (1) use of an estimate of the epicardial potential distribution everywhere on the surface and (2) use of regional bounds on the excursion of the potential. Results indicate that the a posteriori technique called CRESO, developed by Colli Franzone and coworkers, most consistently derives the regularization parameter closest to the optimal parameter for this experimental situation. The sensitivity of the inverse computation in a realistic-geometry torso to inaccuracies in estimating heart position are consistent with results from the eccentric spheres model; errors of 1 cm are well tolerated, but errors of 2 cm or greater result in a loss of position and amplitude information. Finally, estimates and bounds based on accurate, known information successfully lower the relative error associated with the inverse and have the potential to significantly enhance the amplitude and feature position information obtainable from the inverse-reconstructed epicardial potential map.     

Effect of conductivity interfaces

By utilizing an integral equation formulation of Laplace’s equation it is shown that knowledge of the geometry of the conductivity interface, the values of conductivity, and the potentials and gradients on the conductivity interface are sufficient information to determine the infinite media potentials and infinite media potential gradients. The integral equations may be approximated by finite sums and the results can be implemented practically by using a medium size digital computer.     

Decoupled time-marching schemes in computational cardiac electrophysiology and ECG numerical simulation

This work considers the approximation of the cardiac bidomain equations, either isolated or coupled with the torso, via first order semi-implicit time-marching schemes involving a fully decoupled computation of the unknown fields (ionic state, transmembrane potential, extracellular and torso potentials). For the isolated bidomain system, we show that the Gauss-Seidel and Jacobi like splittings do not compromise energy stability; they simply alter the energy norm. Within the framework of the numerical simulation of electrocardiograms (ECG), these bidomain splittings are combined with an explicit Robin-Robin treatment of the heart-torso coupling conditions. We show that the resulting schemes allow a fully decoupled (energy) stable computation of the heart and torso fields, under an additional hyperbolic-CFL like condition. The accuracy and convergence rate of the considered schemes are investigated numerically with a series of numerical experiments.     

A Proposed Method for the Inverse Problem in Electrocardiology

The inverse problem in electrocardiography is considered. A method is proposed in which the cardiac electrical generator is represented by a set of dipoles, fixed in location and direction in order to reflect the known features of myocardial excitation, but variable in strength. A crucial innovation is that since the dipole directions have been so chosen, the dipole strengths must be constrained nonnegative. Surface potentials are measured in vivo and the dipole strengths inferred. In this process, torso models with a varying degree of realism are used. An 11-dipole set is used and potentials are measured at 126 surface locations. For a particular normal subject, the effect of various variables, such as the torso modeling assumptions, on the dipole strengths is investigated. Condensed results are given for twelve normal subjects and two patients.     

The origin of the human auditory brain-stem response wave II

Auditory brain-stem responses (ABRs) were recorded from human subjects undergoing neurosurgical procedures which exposed the auditory nerve. Scalp recordings indicated that the latency of the negativity between waves (I_n) and II (I_n) and the latency of positive peak II (II_p) were shorter when the nerve was suspended in air than when the nerve was submerged in cerebrospinal fluid or saline, while earlier and later waves remained unaffected. These results could not be attributed to changes in stimulus or recording parameters or conduction velocity. Computational and somatosensory experimental evidence of stationary potentials generated by physical properties of the volume conductor, including changes in conductivity or geometry, are presented to develop a model of wave II_p generation. The results of this study suggest that wave II_p (and probably I_n) are manifestations of current flux asymmetries across conductivity boundaries created by the temporal bone-cerebrospinal fluid intradural space-brain-stem interfaces. The current flux asymmetries are generated as the propagating auditory nerve action potential crosses the conductivity boundaries. These results also indicate that the physical characteristics of the volume conductor and neural pathways must be considered when interpreting surface recorded evoked potentials.     

Estimation of breast burn size

It is the authors' opinion that the size of chest burns on large-breasted women can be significantly underestimated, especially if the methods of calculation rely on burn charts, such as the Lund and Browder burns chart. This latter chart is based on data derived from only three women and eight men. The surface area of the torsos of 60 volunteers (20 men, 20 small-breasted women, and 20 large-breasted women) was measured using two well-established techniques. The torso surface area was divided into two parts: the anterior trunk and the posterior trunk (i.e., torso surface area = posterior trunk + anterior trunk). The anterior trunk was subdivided and the area above the costal margins defined as the pectoral region. These areas were measured separately for each individual. The volunteers' total body surface area was calculated using normograms, based on their weight and height. The area of each torso section was recorded as a percentage of the total body surface area and torso surface area. Whereas the torso surface area/total body surface area ratio did not vary significantly between the groups, the proportion of anterior to posterior trunk size did depend on the sex and on breast size. There was a direct correlation between the woman's bra cup size and the ratio of anterior-to-posterior trunk surface area. A simple chart was therefore derived that estimates the relative size of a woman's torso surface area once her bra cup size is known. Such a chart can be used to improve accuracy in adult female chest burn estimation, when used in conjunction with a burns chart. Breast burns in larger breasted women are underestimated when calculated using current burn charts. We recommend that a correction be made when estimating chest burns in women to account for the increased surface area of the breasts. A chart, such as the one we have developed, could be used in conjunction with a burn chart (e.g., Lund and Browder) to make this correction.     

Surface reconstruction of torsos with and without scoliosis

Visible surface asymmetries such as uneven shoulders, waist and hips, shoulder height differences and a shoulder blade prominence are often the most troublesome features associated with adolescent scoliosis. Treatment considerations are influenced by the severity and changes over time of these asymmetries. Outcomes are judged on how well the asymmetries are improved towards a normal trunk shape. In this paper, a deformable self organizing feature map (SOFM) is used as a geometric surface reconstruction tool to model the torso surface of subjects with and without scoliosis. The proposed parameterization technique provides a means of quantifying the surface asymmetries and assessing the changes due to either natural history or the effects of treatment. For evaluation 10 control subjects without scoliosis and 10 adolescents with scoliosis were scanned and their torsos were reconstructed. This preliminary study demonstrates that in around 5 min a torso scan with 60,000 data points can be transformed into a 2562 nodes mesh using SOFM. The accuracy of the final mesh is around 1.40 mm on average. The high accuracy and speed of this technique, makes it well suitable to be used in a clinical setting to assess surface features of subjects with scoliosis.     

Spatial-temporal filter effect in a computer model study of ventricular fibrillation / R?umlicher und zeitlicher Filtereffekt in einer Computermodellstudie zum Herzkammerflimmern

Abstract Prediction of countershock success from ventricular fibrillation (VF) ECG is a major challenge in critical care medicine. Recent findings indicate that stable, high frequency mother rotors are one possible mechanism maintaining VF. A computer model study was performed to investigate how epicardiac sources are reflected in the ECG. In the cardiac tissues of two computer models - a model with cubic geometry and a simplified torso model with a left ventricle - a mother rotor was induced by increasing the potassium rectifier current. On the epicardium, the dominant frequency (DF) map revealed a constant DF of 23 Hz (cubic model) and 24.4 Hz (torso model) in the region of the mother rotor, respectively. A sharp drop of frequency (3-18 Hz in the cubic model and 12.4-18 Hz in the torso model) occurred in the surrounding epicardial tissue of chaotic fibrillatory conduction. While no organized pattern was observable on the body surface of the cubic model, the mother rotor frequency can be identified in the anterior surface of the torso model because of the chosen position of the mother rotor in the ventricle (shortest distance to the body surface). Nevertheless, the DFs were damped on the body surfaces of both models (4.6-8.5 Hz in the cubic model and 14.4-16.4 Hz in the torso model). Thus, it was shown in this computer model study that wave propagation transforms the spatial low pass filtering of the thorax into a temporal low pass. In contrast to the resistive-capacitive low pass filter formed by the tissue, this spatial-temporal low pass filter becomes effective at low frequencies (tens of Hertz). This effect damps the high frequency components arising from the heart and it hampers a direct observation of rapid, organized sources of VF in the ECGs, when in an emergency case an artifact-free recording is not possible.     

The electrostatic potential of B-DNA

Electrostatic potentials around DNA are obtained by solving the nonlinear Poisson-Boltzmann (PB) equation. The detailed charge distribution of the DNA and the different polarizabilities of the macromolecule and solvent are included explicitly in the calculations. The PB equation is solved using extensions of a finite difference approach applied previously to proteins. Electrical potentials and ion concentrations are compared to those obtained with simpler models. It is found that the shape of the dielectric boundary between the macromolecule and solvent has significant effects on the calculated potentials near the surface, particularly in the grooves. Sequence-specific patterns are found, the most surprising result being the existence of positive regions of potential near the bases in both the major and minor grooves. The effect of solvent and ionic atmosphere screening of phosphate-phosphate repulsions is studied, and an effective dielectric function, appropriate for molecular mechanics simulations, is derived.     

Hypothetical model for monitoring microbial growth by using capacitance measurements--a minireview.

Microbiological impedance devices are used routinely by food and manufacturing industries, and public health agencies to measure microbial growth and metabolism. In this paper a hypothetical model explaining the effects of microbial growth and metabolism on capacitance at electrode-medium interfaces, that can be supported by fundamental theories and principles of electrochemistry, is presented. This model provides a framework to interpret changes in capacitance during microbial growth and metabolism and can be used to generate and test hypotheses on factors (i.e., temperature, microbial cell density, microbial growth and medium conductivity) contributing to increases or decreases in capacitance.     

A Mathematical-Physical Model of the Genesis of the Electrocardiogram

A fundamental problem of cardiac electrophysiology is that of relating quantitatively the electrical activity within the heart to the complete timevarying potential distribution at the body surface. A new numerical method is described for the calculation of the surface potential on an irregularly shaped closed external surface due to an arbitrary source distribution in a medium containing regions of different conductivity, subject to the appropriate boundary conditions. The method is intended to provide an exact theoretical analysis of the experimental data acquired by A. M. Scher and others who have been mapping the pathways of ventricular depolarization in dogs and other animals. In anticipation of the above research program, a number of exploratory computations are reported. For example, the surface potential distribution has been calculated for a cylinder of human torso cross-section with a hemispherical dipole layer current source in approximate heart position and orientation and containing “lungs” of conductivity different from that of the surrounding medium. Under certain conditions, when lung-like inhomogeneities are introduced, a simple dipole source can generate a potential distribution having the multiple maxima and minima characteristic of higher multipole sources.     

Investigating the effects of wettability and gaseous nanobubbles on roughened wall–fluid interface using molecular dynamics simulation

This paper reports on the use of molecular dynamics (MD) simulation to investigate the coupling effects of wettability, surface roughness and interfacial nanobubbles (INBs) on wall–fluid interfaces. The fluid properties close to the wall–fluid interface, such as potential energy, density, diffusion coefficients of fluid molecules and effective slip length are simulated. In the cases without surface nanobubbles, regions with lower potential energy have a higher probability of hosting water molecules. The local translational and rotational diffusion coefficients of water within the cavities are strongly influenced by wettability but largely unaffected by hydrodynamic effects. In cases where INBs exist, variations in wettability result in distinctly different argon morphologies. Argon nanobubbles form a convex shape on Wenzel-like interfaces but a shallow concave shape on Cassie-like interfaces. The phenomenon of water molecules invading grooves tends to occur on Wenzel-like interfaces; however, this depends largely on the morphology of the grooves. The high mobility and high density of argon molecules indicate that the state of the argon molecules within the grooves may require further investigation. Our results also show that the effective slip length is significantly influenced by wall–fluid wettability as well as the morphology of INBs.