Noninvasive assessment of local myocardium repolarization changes using high resolution surface ECG mapping

A method using body surface potential maps for assessment of myocardium lesions with changed repolarization is presented and suitable mapping system is introduced. Differences between normal and altered QRST integral maps together with torso volume conductor model were used to determine the equivalent dipole representing the lesion. Performance of the method was studied on simulated data. Changed repolarization was modeled by shortening of myocyte action potentials in regions typical for stenosis of the main coronary arteries. The equivalent dipole estimated the positions of small lesions with a mean error of 9+/-4 mm (17+/-14 mm for larger transmural lesions). The subepicardial or subendocardial character of the lesions was reflected in the dipole orientation. Tests of the method on patients after myocardial infarction that underwent coronary intervention on a single coronary vessel showed that in 7 of 8 successfully treated patients the dipole position matched well with the treated vessel. A small dipole moment in another patient indicated unsuccessful treatment. The method was implemented in a new 128-channel mapping system. Its active electrodes, battery powered measuring unit and optical computer interface help to minimize noise in ECG and guarantee patient's safety. The results suggest that the method and mapping system offer useful tools for noninvasive identification of local repolarization changes in the myocardium.     

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.     

All-valence-shell molecular orbital calculations on the chiroptical properties of substituted and unsubstituted 2,5-diketopiperazine structures

The chiroptical properties of L -3-methyl-2,5-diketopiperazine (L -alanylglycyl anhydride) are examined on a theoretical model in which the electronic wave functions are obtained from semi-empirical all-valence-shell molecular orbital calculations. The INDO molecular orbital model is used to perform SCF-MO calculations on the ground states of six conformation isomers of L -3-methyl-2,5-diketopiperazine and two chiral conformational isomers of unsubstituted 2,5-diketopiperazine. Excited-state wave functions are constructed in the virtual orbital-configuration interaction approximation. The rotatory strengths, dipole strengths, oscillator strengths, and dissymmetry factors of the first eight singlet–singlet transitions for each of the eight structures are calculated and reported. Additionally, ground-state dipole moments, net atomic charges, and the first four ionization potentials (calculated according to Koopman's theorem) are computed for each structure. The signs and the magnitudes of the rotatory strengths are found to be extremely sensitive to the conformation of the piperazine ring as well as to methyl substitution at the α carbon of the ring. Spectra–structure relationships based on the calculations reported here are discussed, and the available experimental CD data on dissymmetric 2,5-diketopiperazine are examined in terms of our theoretical results.     

The inconsistencies of present-day mathematical-physical methods pertaining to current generators in volume conductors used in electrocardiography

The present-day practices of electrocardiography and vectorardiography are based upon the theory that the surface potential differences can be assumed to be due to a single dipole inside the body. It is shown in this paper that a dipole cannot account for all the surface potentials due to realistic current generators, and hence the determination of the current generator from surface potential measurements based upon such a theory will lead to inconsistent representations of the heart for one and the same subject. To demonstrate this point two eccentric dipoles of different strengths and locations representing two muscle fibers are taken to be the current generator in a homogeneous spherical conductor. The exact surface potentials are then expressed by means of the “interior sphere theorem” of the authors. With these expressions the magnitude, direction, and location of the resultant dipole are determined by the method of D. Gabor and C. V. Nelson (J. App. Physics,25, 413–16, 1954). The surface potentials due to this resultant dipole are again exactly expressed by means of the “interior sphere theorem” and compared with those due to the eccentric dipoles assumed. It can be seen that the differences can be considerable. It is suggested that the multipole model of the authors (Bull. Math. Biophysics,20, 203–16, 1958) be used as a more accurate and the only unique representation of the heart. This investigation was supported by the National Heart Institute under a research grant H-2263(c).     

How pore mouth charge distributions alter the permeability of transmembrane ionic channels.

This paper investigates the effects that surface dipole layers and surface charge layers along the pore mouth-water interface can have on the electrical properties of a transmembrane channel. Three specific molecular sources are considered: dipole layers formed by membrane phospholipids, dipole layers lining the mouth of a channel-forming protein, and charged groups in the mouth of a channel-forming protein. We find, consistent with previous work, that changing the lipid-water potential difference only influences channel conduction if the rate-limiting step takes place well inside the channel constriction. We find that either mouth dipoles or mouth charges can act as powerful ion attractors increasing either cation or anion concentration near the channel entrance to many times its bulk value, especially at low ionic strengths. The effects are sufficient to reconcile the apparently contradictory properties of high selectivity and high conductivity, observed for a number of K+ channel systems. We find that localizing the electrical sources closer to the constriction entrance substantially increases their effectiveness as ion attractors; this phenomenon is especially marked for dipolar distributions. An approximate treatment of electrolyte shielding is used to discriminate between the various mechanisms for increasing ionic concentration near the constriction entrance. Dipolar potentials are far less sensitive to ionic strength variation than potentials due to fixed charges. We suggest that the K+ channel from sarcoplasmic reticulum does not have a fixed negative charge near the constriction entrance; we suggest further that the Ca+2-activated K+ channel from transverse tubule does have such a charge.     

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     

Capacitance and conductance as tools for the measurement of asymmetric surface potentials and energy barriers of lipid bilayer membranes

Summary A simple method for the determination of asymmetric surface potentials in lipid bilayers is described. The method is based on the dependence of bilayer capacitance on transmembrane voltage. The capacitance is measured by rectifying the 90° component of an applied alternating current signal. A superimposed slow triangular wave results in a hysteresis-like time course of capacitance. The center of the hysteresis figure is shifted along the voltage axis by an amount equal to the difference of the dipole plus surfacecharge potentials on the two sides of the bilayer (capacitance minimization potential).Alternatively, such bilayer asymmetry was studied by using the current-voltage characteristics in the presence of nonactin as a carrier. This analysis was based on the integrated Nernst-Planck equation, assuming a trapezoidal energy barrier and equilibrium of the surface reactions.The two methods gave consistent results for the surface potentials of phosphatidyl serine membranes asymmetrically shielded with calcium. In addition, the current analysis yields the positions of the corners of the barrier, found to be set in 13% for this lipid.     

Effect of gramicidin A on the dipole potential of phospholipid membranes.

The effect of channel-forming peptide gramicidin A on the dipole potential of phospholipid monolayers and bilayers has been studied. Surface pressure and surface potential isotherms of monolayers have been measured with a Langmuir trough equipped with a Wilhelmy balance and a surface potential meter (Kelvin probe). Gramicidin has been shown to shift pressure-area isotherms of phospholipids and to reduce their monolayer surface potentials. Both effects increase with the increase in gramicidin concentration and depend on the kind of phosphatidylcholine used. Application of the dual-wavelength ratiometric fluorescence method using the potential-sensitive dye RH421 has revealed that the addition of gramicidin A to dipalmitoylphosphatidylcholine liposomes leads to a decrease in the fluorescence ratio of RH421. This is similar to the effect of phloretin, which is known to decrease the dipole potential. The comparison of the concentration dependences of the fluorescence ratio for gramicidin and phloretin shows that gramicidin is as potent as phloretin in modifying the membrane dipole potential.     

Genetic algorithm-neural network estimation of cobb angle from torso asymmetry in scoliosis

Scoliosis severity, measured by the Cobb angle, was estimated by artificial neural network from indices of torso surface asymmetry using a genetic algorithm to select the optimal set of input torso indices. Estimates of the Cobb angle were accurate within 5 degrees in two-thirds, and within 10 degrees in six-sevenths, of a test set of 115 scans of 48 scoliosis patients, showing promise for future longitudinal studies to detect scoliosis progression without use of X-rays.     

A note on dipole sources in conducting biological tissues

The study of current flow fields in biologicaltissue requires finding the potential field from dipole sources such that the normal gradient vanishes at the exterior surface. A convenient way to determine the dipole field is by taking the gradient of the potential field set up by a point source. However, the point source problem is ill-posed when the normal gradient is required to vanish at the outer surface. In the paper the nature of this problem is discussed and several methods for overcoming the difficulty are presented.     

The effects of heart-cavity blood resistivity and volume on endocardial potentials: theoretical predictions

Theoretical concepts regarding the potential variations within the bloodfilled cavities of the heart caused by excitation of the myocardium are scarce. In an attempt to understand these potential variations, calculations were made of the potentials due to a dipole adjacent to a disk of finite resistivity. The dipole was assumed to be in an infinite two-dimensional medium of higher resistivity. Equations for the potential inside a sphere due to an external source are also given.On the basis of the results, predictions were made on the effects of the intracardiac blood on the endocardial potentials: (1) the potential at the center of the cavity is independent of blood resistivity and equivalent to the free space potential; (2) potentials due to a tangential dipole are uniformly reduced; (3) potentials due to a radial dipole are smaller near the dipole, but greater at the far end of the dipole axis; (4) for a dipole radial to or making an angle with the cavity, potentials are reduced at some points but increased at others; (5) the potential along the transverse axis of the dipole has a constant value depending on conductivity; (6) intracardiac blood tends to smooth out potential variations within the cavity; (7) the potential depends both on dipole distance and direction; and (8) if the cavity volume increases, potentials decrease with distance from the dipole; the potential at the adjacent endocardial wall changes little.     

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.     

Effect of conductivity interfaces in electrocardiography

This paper develops numerical techniques for two problems of interest in electrocardiography: (1) the determination of infinite-media surface potential gradients from boundedmedia torso potentials, and (2) the effects of lung-torso, blood mass-torso, and torso-air conductivity interfaces on torso surface potentials. This paper is an extension of a previous paper on the effects of conductivity interfaces which also utilized an integral equation formulation of Laplace's equation. Supported in part by USPHS Grants HE 05716 and HE 11307 and American Heart Grant 67-850.     

Nicotinic acetylcholine receptor channel electrostatics determined by diffusion-enhanced luminescence energy transfer

The electrostatic potentials within the pore of the nicotinic acetylcholine receptor (nAChR) were determined using lanthanide-based diffusion-enhanced fluorescence energy transfer experiments. Freely diffusing Tb3+ -chelates of varying charge constituted a set of energy transfer donors to the acceptor, crystal violet, a noncompetitive antagonist of the nAChR. Energy transfer from a neutral Tb3+ -chelate to nAChR-bound crystal violet was reduced 95% relative to the energy transfer to free crystal violet. This result indicated that crystal violet was strongly shielded from solvent when bound to the nAChR. Comparison of energy transfer from positively and negatively charged chelates indicate negative electrostatic potentials of -25 mV in the channel, measured in low ionic strength, and -10 mV measured in physiological ionic strength. Debye-Hückel analyses of potentials determined at various ionic strengths were consistent with 1-2 negative charges within 8 A of the crystal violet binding site. To complement the energy transfer experiments, the influence of pH and ionic strength on the binding of [3H]phencyclidine were determined. The ionic strength dependence of binding affinity was consistent with -3.3 charges within 8 A of the binding site, according to Debye-Hückel analysis. The pH dependence of binding had an apparent pKa of 7.2, a value indicative of a potential near -170 mV if the titratable residues are constituted of aspartates and glutamates. It is concluded that long-range potentials are small and likely contribute little to selectivity or conductance whereas close interactions are more likely to contribute to electrostatic stabilization of ions and binding of noncompetitive antagonists within the channel.     

The influence of conductivity changes in boundary element compartments on the forward and inverse problem in electroencephalography and magnetoencephalography.

Source localization based on magnetoencephalographic and electroencephalographic data requires knowledge of the conductivity values of the head. The aim of this paper is to examine the influence of compartment conductivity changes on the neuromagnetic field and the electric scalp potential for the widely used three compartment boundary element models. Both the analysis of measurement data and the simulations with dipoles distributed in the brain produced two significant results. First, we found the electric potentials to be approximately one order of magnitude more sensitive to conductivity changes than the magnetic fields. This was valid for the field and potential topology (and hence dipole localization), and for the amplitude (and hence dipole strength). Second, changes in brain compartment conductivity yield the lowest change in the electric potentials topology (and hence dipole localization), but a very strong change in the amplitude (and hence in the dipole strength). We conclude that for the magnetic fields the influence of compartment conductivity changes is not important in terms of dipole localization and strength estimation. For the electric potentials however, both dipole localization and strength estimation are significantly influenced by the compartment conductivity.     

Electrostatics and electrodynamics of bacteriorhodopsin.

The stationary electric dichroism of bacteriorhodopsin is in qualitative, but not quantitative, agreement with the orientation function for disks having a permanent dipole directed perpendicular to the plane and an induced dipole in the plane. Fits of the orientation function to data measured at low field strengths demonstrate: an increase of the permanent dipole moment mu with the square of the disk radius r2, whereas the polarizability alpha increases with r4; the ionic strength dependence is small for mu and clearly stronger for alpha; the permanent dipole moment is 4x10(6) D at r = 0.5 micron. According to the risetime constants, the induced dipole does not saturate and increases to 4x10(8) D at 40 kV/cm and r = 0.5 micron. The data indicate that the permanent dipole is not of some interfacial character but is due to a real assymetry of the charge distribution. The experimental dipole moment per protein monomer is approximately 55 D, whereas calculations based on the structure of Grigorieff et al. (Grigorieff, N., T.A. Ceska, K.H. Downing, J.M. Baldwin, and R. Henderson. 1996. Electron-crystallographic refinement of the structure of bacteriorhodopsin. J. Mol. Biol. 259:393-421) provide a dipole moment of approximately 570 D. The difference is probably due to a nonsymmetric distribution of charged lipid residues. It is concluded that experimental dipole moments reflect the mu-potential at the plane of shear for rotational diffusion, in analogy to the sigma-potential used for translational diffusion. It is suggested that the permanent dipole of bacteriorhodopsin supports proton transport by attraction of protons inside and repulsion of protons outside of the cell. Dichroism rise curves at field strengths between E = 150 and 800 V/cm reveal an exponential component with time constants tau 3r in the range between 1 and 40 ms, which is not found in Brownian dynamics simulations on a disk structure using hydrodynamic and electric parameters characteristic of bacteriorhodopsin disks. The experimental data suggest that this process reflects a cooperative change of the bacteriorhodopsin structure, which is induced already at a remarkably low field strength of approximately 150 V/cm.     

Electrostatic potentials of the alpha helix dipole and of elastase

Molecular graphics has been used to display the electrostatic potentials of the α-helix dipole and that of elastase calculated using atomic charges obtained by a new, simple method^1–3. Calculations on the α-helix dipole support the simple dipole model in which the helix is represented by single, half integral charges at the helix termini. The potentials of elastase show some interesting features which may be related to the binding processes.     

Internal electrostatic potentials in bilayers: measuring and controlling dipole potentials in lipid vesicles.

The binding and translocation rates of hydrophobic cation and anion spin labels were measured in unilamellar vesicle systems formed from phosphatidylcholine. As a result of the membrane dipole potential, the binding and translocation rates for oppositely charged hydrophobic ions are dramatically different. These differences were analyzed using a simple electrostatic model and are consistent with the presence of a dipole potential of approximately 280 mV in phosphatidylcholine. Phloretin, a molecule that reduces the magnitude of the dipole potential, increases the translocation rate of hydrophobic cations, while decreasing the rate for anions. In addition, phloretin decreases the free energy of binding of the cation, while increasing the free energy of binding for the anion. The incorporation of 6-ketocholestanol also produces differential changes in the binding and translocation rates of hydrophobic ions, but in an opposite direction to those produced by phloretin. This is consistent with the view that 6-ketocholestanol increases the magnitude of the membrane dipole potential. A quantitative analysis of the binding and translocation rate changes produced by ketocholestanol and phloretin is well accounted for by a point dipole model that includes a dipole layer due to phloretin or 6-ketocholestanol in the membrane-solution interface. This approach allows dipole potentials to be estimated in membrane vesicle systems and permits predictable, quantitative changes in the magnitude of the internal electrostatic field in membranes. Using phloretin and 6-ketocholestanol, the dipole potential can be altered by over 200 mV in phosphatidylcholine vesicles.     

Carcinoma and SV40-Transfected Normal Ovarian Surface Epithelial Cell Comparison by Nonphotochemical Hole Burning

Results are presented of nonphotochemical-hole-burning experiments on the mitochondrial specific dye rhodamine 800 incubated with two human ovarian surface epithelial cell lines: OSE(tsT)-14 normal cells and OV167 carcinoma cells. This dye is selective for the plasma and inner membranes of the mitochondria, as shown by confocal microscopy images. Dispersive hole-growth kinetics of zero-phonon holes are analyzed with theoretical fits, indicating that subcellular structural heterogeneity of the carcinoma cell line is lower relative to the analogous normal cell line. Broadening of holes in the presence of an applied electric field (Stark effect) was used to determine the permanent dipole moment change for the S₀→S₁ transition in the two cell lines. For the carcinoma cell line, the permanent dipole moment change value is a factor of 1.5 higher than for the normal cell line. It is speculated that this difference may be related to differences in mitochondrial membrane potentials in the two cell lines.