A method for determining the heart moving electric center on surface distributed models of the cardioelectric generator

Using mathematical models of the bioelectric generators of the heart with surface distributed configurations, it was shown that the coordinates of the moving electric center of the heart can facilitate the recognition of the global spatial position of electrogenic zones in the myocardium. These coordinates were determined by the previously proposed method from the cardioelectric potential measured noninvasively with a multichannel lead system in the framework of electrocardiographic mapping.     

Correlation in time of the process of cardiac ventricle intramural depolarization and of distribution of cardioelectric field potentials of the dog <Emphasis Type="Italic">Canis famjliaris</Emphasis>

Based on a multichannel synchronous mapping of heart electric potentials, the sequence in time of the ventricle myocardium depolarization was compared with dynamics of distribution of cardioelectric potentials on the dog body surface. The cardioelectric field on the dog body surface at the period of the initial ventricular activity has been shown to be characterized by the presence of two inversions of the mutual disposition of areas of positive and negative potentials. Contribution to formation of distribution of the cardioelectric potentials on the body surface at each moment of the period of initial ventricular activity was made by all myocardial layers involved in excitation.     

Correlation in the of the process of cardiac ventricle intramural depolarization and distribution of cardioelectric field potentials of the dog Canis familiaris

Based on a multichannel synchronous mapping of heart electric potentials, the sequence in time of the ventricle myocardium depolarization was compared with dynamics of distribution of cardioelectric potentials on the body surface in a dog. The cardioelectric field on the dog body surface at the period of the initial ventricular activity has been shown to be characterized by the presence of two inversions of the mutual disposition of areas of positive and negative potentials. Contribution to formation of distribution of the cardioelectric potentials on the body surface at each moment of the period of initial ventricular activity was made by all myocardial layers involved by excitation.     

Relation of growth process to spatial patterns of electric potential and enzyme activity in bean roots

The electric spatial pattern and invertase activity distribution in growing roots of azuki bean (Phaseolus chrysanthos) have been studied. The electric potential near the surface along the root showed a banding pattern with a spatial period of about 2 cm. It was found that the enzyme activity has a peak around 3-7 mm from the root tip, in good agreement with the position of the first peak of the electric potential, which is located a little behind the elongation zone. An inhomogeneous distribution of ATP content was also detected along the root. Experiments on the electric isolation of the elongation zone from the mature zone and acidification treatment showed that H+ is transported from the mature-side to elongation-side regions, causing tip elongation through an acid-growth mechanism. Both acidification and electric disturbance on growing roots affected growth significantly. Simultaneous measurements of electric potential and enzyme activity clearly showed a good correlation between these two quantities and growth speed. From an analogy with the Characean banding, the spatio-temporal organization via the cell membrane in electric potential and enzyme activity can be regarded as a dissipative structure arising far from equilibrium. These experimental results can be interpreted with a new mechanism that the dissipative structure is formed spontaneously along the whole root, accompanied by energy metabolism, to make H+ flow into the root tip.     

Cardiac electric field at the period of depolarization and repolarization of the frog heart ventricle

Multichannel mapping of electrical field on heart ventricle epicardium and the body surface in frogs Rana esculenta and Rana temporaria was performed at periods of the ventricular myocardium depolarization and repolarization. The zone of the epicardium early depolarization is located on epicardium of the ventricle base posterior wall, while the late depolarization zone--on its apex and on the base anterior wall. The total vector of sequence of the ventricle epicardium depolarization is directed from the base to the apex. The zone of the early repolarization is located in the apical area, while that of the late one--in the area of the base. On the frog body surface the cardioelectric field with the cranial zone of negative and the caudal zone of positive potentials is formed before the appearance of the QRS complex on ECG. At the period of the heart ventricle repolarization the zone of the cardioelectric field negative potentials is located in the cranial, while that of the positive ones--in the body surface caudal parts. The cardioelectric field on the frog body surface at the periods of depolarization and repolarization of the ventricle myocardium reflects adequately the projection of sequence of involvement with excitation and of distribution of potentials on epicardium.     

Cardiac electric field at the period of depolarization and repolarization of the frog heart ventricle

Multichannel mapping of electrical field on heart ventricle epicardium and the body surface in frogs Rana esculenta and Rana temporaria was performed at periods of the ventricular myocardium depolarization and repolarization. The zone of the epicardium early depolarization is located on epicardium of the ventricle base posterior wall, while the late depolarization zone—on its apex and on the base anterior wall. The total vector of sequence of the ventricle epicardium depolarization is directed from the base to the apex. The zone of the early repolarization is located in the apical area, while that of the late one—in the area of the base. On the frog body surface the cardioelectric field with the cranial zone of negative and the caudal zone of positive potentials is formed before the appearance of the QRS complex on ECG. At the period of the heart ventricle repolarization the zone of the cardioelectric field negative potentials is located in the cranial, while that of the positive ones—in the body surface caudal parts. The cardioelectric field on the frog body surface at the periods of depolarization and repolarization of the ventricle myocardium reflects adequately the projection of sequence of involvement with excitation and of distribution of potentials on epicardium.     

Generation of electric current by chromatophores of Rhodospirillum rubrum and reconstitution of electrogenic function in subchromatophore pigment-protein complexes.

Lipoprotein complexes, containing (1) bacteriochlorophyll reaction centers, (2) bacteriochlorophyll light-harvesting antenna or (3) both reaction centers and antenna, have been isolated from chromatophores of non-sulphur purple bacteria Rhodospirillum rubrum by detergent treatments. The method of reconstituting the proteoliposomes containing these complexes is described. Being associtated with planas azolectin membrane, ptoteoliposomes as well as intact chromatophores were found to generate a light-dependent transmembrane electric potential difference measured by Ag/AgC1 electrodes and voltmeter. The direction of the electric field inproteoliposomes can be regulated by the addition of antenna complexes to the reconstitution mixture. The reaction center complex proteoliposomes generate an electric field of a direction opposite to that in chromatophores, whereas proteoliposomes containing reaction center complexes and a sufficient amount of antenna complexes produce a potential difference as in chromatophores. ATP and inorganic pyrophosphate, besides light, were shown to be usable as energy sources for electric generation in chromatophores associated with planar membrane.     

Generation of electric current by chromatophores of Rhodospirillum rubrum and reconstitution of electrogenic function in subchromatophore pigment-protein complexes

Lipoprotein complexes, containing (1) bacteriochlorophyll reaction centers, (2) bacteriochlorophyll light-harvesting antenna or (3) both reaction centers and antenna, have been isolated from chromatophores of non-sulphur purple bacteria Rhodospirillum rubrum by detergent treatments. The method of reconstituting the proteoliposomes containing these complexes is described. Being associated with planar azolectin membrane, proteoliposomes as well as intact chromatophores were found to generate a light-dependent transmembrane electric potential difference measured by Ag/AgCl electrodes and voltmeter. The direction of the electric field in proteoliposomes can be regulated by the addition of antenna complexes to the reconstitution mixture. The reaction center complex proteoliposomes generate an electric field of a direction opposite to that in chromatophores, whereas proteoliposomes containing reaction center complexes and a sufficient amount of antenna complexes produce a potential difference as in chromatophores. ATP and inorganic pyrophosphate, besides light, were shown to be usable as energy sources for electric generation in chromatophores associated with planar membrane.     

The intraglobular electrostatic field of an enzyme. 1. The primary field created by the polypeptide core, functional groups and ions of the alpha-chymotrypsin molecule

The electric field set up by the dipoles of peptide groups ad other dipoles at the atoms of substrate and catalytic groups of alpha-chymotrypsin is considered. It is shown that substantial electric potentials reaching some tenths of volts exist in the active center of the enzyme, the fact which must influence significantly the reactivity of corresponding groups. In contrast to low molecular weight liquids, the contribution to the total potential of dipoles located at different distances from the point under consideration often changes nonmonotonically with the distance, sometimes the predominant influence being exerted not by the nearest polar groups but by the more distant ones. The existence of electric fields having a complex spatial configuration determined by the protein structure can be defined as the effect of the polar medium preorganization. Emphasis is placed on the necessity of taking into account the polarization of the external medium by charges of protein atoms and ions (the difference of primary and secondary electric fields).     

Oscillations of electric spatial patterns emerging from the homogeneous state in characean cells

Electric spatial patterns of bands formed along the cell wall of the characean internode were studied using a multi-electrode measuring system. The electric potential near the surface of the cell was measured by arranging about 25 electrodes along the cell at approximately 1.6 mm intervals. Since the time required for one scan over the cell length is only 1 s, the temporal change in the spatial pattern of surface electric potential can be readily observed. Oscillations were sometimes found as the electric pattern started to appear after the cell was illuminated. Fourier analysis shows that a single spatial mode arises gradually and then becomes stabilized in an oscillatory manner. A simple electric circuit model comprising three variables, i.e., a membrane potential, an electric current across the membrane and an electromotive force, can simulate well the oscillatory rise of bands. These results imply that the electric spatial pattern observed in characean internodes is a self-organized structure emerging far from equilibrium, known as a dissipative structure. Biophysical mechanisms of band formation are discussed.     

Band structure of surface electric potential in growing roots

For growing roots of azuki bean (Phaseolus chrysanthos), an electric potential is measured minutely along the surface of the root, together with the surface pH. It was found that the root begins to display a band-type pattern of potential with a spatial period of about 2 cm in a mature region as soon as it grows to about 10 cm in root length, while the surface potential shows only one convex peak around a position 5-20 mm behind a root tip and a succeeding concave peak around 20-35 mm, providing the length of root is shorter than about 10 cm. Since the surface potential takes a relatively positive value on average at the side of the root base compared with that in an elongation zone near the tip, electric current is supposed to flow into the elongation zone, accompanied by some local current loops in the mature region. The present band-type pattern observed first in multi-cell systems seems to be a kind of dissipative structure appearing far from equilibrium, and hence its relationship to growth is discussed.     

Electrostatic potential and Born energy of charged molecules interacting with phospholipid membranes: calculation via 3-D numerical solution of the full Poisson equation.

Understanding the physicochemical basis of the interaction of molecules with lipid bilayers is fundamental to membrane biology. In this study, a new, three-dimensional numerical solution of the full Poisson equation including local dielectric variation is developed using finite difference techniques in order to model electrostatic interactions of charged molecules with a non-uniform dielectric. This solution is used to describe the electric field and electrostatic potential profile of a charged molecule interacting with a phospholipid bilayer in a manner consistent with the known composition and structure of the membrane. Furthermore, the Born interaction energy is then calculated by appropriate integration of the electric field over whole space. Numerical computations indicate that the electrostatic potential profile surrounding a charge molecule and its resultant Born interaction energy are a function of molecular position within the membrane and change most significantly within the polar region of the bilayer. The maximum interaction energy is observed when the charge is placed at the center of the hydrophobic core of the membrane and is strongly dependent on the size of the charge and on the thickness of the hydrocarbon core of the bilayer. The numerical results of this continuum model are compared with various analytical approximations for the Born energy including models established for discontinuous slab dielectrics. The calculated energies agree with the well-known Born analytical expression only when the charge is located near the center of a hydrocarbon core of greater than 60 A in thickness. The Born-image model shows excellent agreement with the numerical results only when modified to include an appropriate effective thickness of the low dielectric region. In addition, a newly derived approximation which considers the local mean dielectric provides a simple and continuous solution that also agrees well with the numerical results.     

基于RS与水动力模型的鄱阳湖草洲产卵型鱼类潜在产卵场识别

鱼类产卵场的研究与保护对维持鱼类生物多样性具有重要意义,研究结合遥感数据与水动力模型,旨在识别2000—2020年鄱阳湖草洲产卵型鱼类潜在产卵场,并分析其时空变化特征,探究现有保护区对产卵场的保护效率。结果表明,近20年来鄱阳湖鱼类潜在产卵场面积呈增加趋势,空间上呈现从湖岸向中心扩张趋势。2005年前后潜在产卵场平均面积分别为519.97和694.42 km²,产卵场面积与空间分布均发生显著变化。2005年前潜在产卵场主要分布于鄱阳湖西部的永修、新建,以及东部的鄱阳和南部的余干等地近岸区域。2005年之后产卵场向湖中心扩张,都昌水域出现大片连续的潜在产卵场。鄱阳湖鲤鲫产卵场省级自然保护区内平均包含了17.75%的潜在产卵场,鄱阳湖的蝶形湖平均分布有34.73%的潜在产卵场。潜在产卵场分布可以进一步指导鄱阳湖保护区的优化和鱼类产卵场调查,研究使用的方法也适用于其他区域草洲产卵型鱼类潜在产卵场的识别研究。     

Electric field interactions in pairs of electric fish: modeling and mimicking naturalistic inputs

Weakly electric fish acquire information about their surroundings by detecting and interpreting the spatial and temporal patterns of electric potential across their skin, caused by perturbations in a self-generated, oscillating electric field. Computational and experimental studies have focused on understanding the electric images due to simple, passive objects. The present study considers electric images of a conspecific fish. It is known that the electric fields of two fish interact to produce beats with spatially varying profiles of amplitude and phase. Such patterns have been shown to be critical for electrosensory-mediated behaviours, such as the jamming avoidance response, but they have yet to be well described. We have created a biophysically realistic model of a wave-type weakly electric fish by using a genetic algorithm to calibrate the parameters to the electric field of a real fish. We use the model to study a pair of fish and compute the electric images of one fish onto the other at three representative phases within a beat cycle. Analysis of the images reveals rostral/caudal and ipsilateral/contralateral patterns of amplitude and phase that have implications for localization of conspecifics (both position and orientation) and communication between conspecifics. We then show how the common stimulation paradigm used to mimic a conspecific during in vivo electrophysiological experiments, based on a transverse arrangement of two electrodes, can be improved in order to more accurately reflect the important qualitative features of naturalistic inputs, as revealed by our model.     

Costs and benefits of within-group spatial position: a feeding competition model

An animal's within-group spatial position has several important fitness consequences. Risk of predation, time spent engaging in antipredatory behavior and feeding competition can all vary with respect to spatial position. Previous research has found evidence that feeding rates are higher at the group edge in many species, but these studies have not represented the entire breadth of dietary diversity and ecological situations faced by many animals. In particular the presence of concentrated, defendable food patches can lead to increased feeding rates by dominants in the center of the group that are able to monopolize or defend these areas. To fully understand the tradeoffs of within-group spatial position in relation to a variety of factors, it is important to be able to predict where individuals should preferably position themselves in relation to feeding rates and food competition. A qualitative model is presented here to predict how food depletion time, abundance of food patches within a group, and the presence of prior knowledge of feeding sites affect the payoffs of different within-group spatial positions for dominant and subordinate animals. In general, when feeding on small abundant food items, individuals at the front edge of the group should have higher foraging success. When feeding on slowly depleted, rare food items, dominants will often have the highest feeding rates in the center of the group. Between these two extreme points of a continuum, an individual's optimal spatial position is predicted to be influenced by an additional combination of factors, such as group size, group spread, satiation rates, and the presence of producer-scrounger tactics.     

Phase and amplitude maps of the electric organ discharge of the weakly electric fish,Apteronotus leptorhynchus

Summary The electric organ discharge (EOD) potential was mapped on the skin and midplane of several Apteronotus leptorhynchus. The frequency components of the EOD on the surface of the fish have extremely stable amplitude and phase. However, the waveform varies considerably with different positions on the body surface. Peaks and zero crossings of the potential propagate along the fish's body, and there is no point where the potential is always zero. The EOD differs significantly from a sinusoid over at least one third of the body and tail. A qualitative comparison between fish showed that each individual had a unique spatiotemporal pattern of the EOD potential on its body.The potential waveforms have been assembled into high temporal and spatial resolution maps which show the dynamics of the EOD. Animation sequences and Macintosh software are available by anonymous ftp (mordor.cns.caltech.edu; cd/pub/ElectricFish).We interpret the EOD maps in terms of ramifications on electric organ control and electroreception. The electrocytes comprising the electric organ do not all fire in unison, indicating that the command pathway is not synchronized overall. The maps suggest that electroreceptors in different regions fulfill different computational roles in electroreception. Receptor mechanisms may exist to make use of the phase information or harmonic content of the EOD, so that both spatial and temporal patterns could contribute information useful for electrolocation and communication.Abbreviations EOD electric organ discharge - EO electric organ - CV coefficient of variance     

On the theory of diffusion of electrolytes

In the theory of diffusion of electrolytes the following assumptions are frequently made: (i) the electrolytic solution is electrically neutral everywhere, (ii) the ionic concentrations and the electric potential all depend on a single Cartesian coordinate as the only space variable. Often the electric potential of the solution is determined on the basis of the Poisson equation alone, disregarding any other relation between this potential and the ionic concentrations. Since the Poisson equation only represents a condition which the potential fulfills, the use of this equation alone may lead to error unless the explicit relation for the potential involving a space integration of ionic concentrations is also taken into account. But if this relation is used the Poisson equation becomes redundant and, more important, assumptions (i) and (ii) appear unacceptable, the former because it leads to a zero electric potential everywhere, the latter because it is mathematically incorrect. The present paper is based on general equations of diffusion of ions, excluding the Poisson equation. These equations form a system of nonlinear integrodifferential quations whose number equals the number of ionic species present in the solution. It appears that when all ions are distributed symmetrically around a point all functions related to the above system of equations can be made dependent on a single space coordinate: the distance from the center of symmetry. Two methods of successive approximations are given for the solution of the equations in the case of spherical symmetry with limitation to the steady state. These methods are then applied to the study of the distribution of ionic concentrations and electrical potentials inside a cell of spherical shape in equilibrium with its surroundings. These methods are rapidly convergent; exact theoretical values of the electric potential are calculable on the boundary of the cell. It appears that the potential at the center of the cell is not more than ∼50% higher than at its boundary and that variation of concentration inside the cell is not very large. For instance, with 100 mV on the boundary the ionic concentration there is about four times higher than at the center. Calculations show that extremely small amounts of electricity are sufficient to account for the electric potentials currently observed. In a cell of 100 micra diameter an average concentration of only 10⁻¹⁴ mole/cm³ of a monovalent ion would be sufficient to give 1 millivolt on the boundary. This concentration is directly proportional to the voltage and inversely proportional to the square of the cell diameter. Most of the numerical results given above are obtained by considering only those ions whose electrical charge is not compensated for by ions of an opposite sign. The total concentrations may be much higher than those quoted. The theory does not take into account possible effects of structural heterogeneities which may exist in the cell, particularly of various phase boundaries. An incidental result shows that the Boltzmann distribution function in the form employed in modern theory of electrolytes is fundamentally a consequence of the mathematical theory of diffusion alone. It is pointed out, however, that Boltzmann distribution is not always compatible with the definition of the electric potential.     

Electric field and current density distribution in an anatomical head model during transcranial direct current stimulation for tinnitus treatment

Tinnitus is considered an auditory phantom percept. Recently, transcranial direct current stimulation (tDCS) has been proposed as a new approach for tinnitus treatment including, as potential targets of interest, either the temporal and temporoparietal cortex or prefrontal areas. This study investigates and compares the spatial distribution of the magnitude of the electric field and the current density in the brain tissues during tDCS of different brain targets. A numerical method was applied on a realistic human head model to calculate these field distributions in different brain structures, such as the cortex, white matter, cerebellum, hippocampus, medulla oblongata, pons, midbrain, thalamus, and hypothalamus. Moreover, the same distributions were evaluated along the auditory pathways. Results of this study show that tDCS of the left temporoparietal cortex resulted in a widespread diffuse distribution of the magnitude of the electric fields (and also of the current density) on an area of the cortex larger than the target brain region. On the contrary, tDCS of the dorsolateral prefrontal cortex resulted in a stimulation mainly concentrated on the target itself. Differences in the magnitude distribution were also found on the structures along the auditory pathways. A sensitivity analysis was also performed, varying the electrode position and the human head models. Accurate estimation of the field distribution during tDCS in different regions of the head could be valuable to better determine and predict efficacy of tDCS for tinnitus suppression.     

多源空间数据整合视角下的城市开发强度研究

城市开发强度能直观表征人类活动强度,对指导城市规划与管理、促进城市可持续发展具有重要价值。采用社会-经济-生态系统耦合视角构建城市开发强度的多维测度体系,整合多源空间数据,测度了杭州市主城及3个副城的开发强度并揭示了其空间分布特征。结果表明,杭州城市开发强度由主城向副城呈波动降低,高强度开发过度集中于主城,主城的功能疏散有待加强;各副城开发强度不一,江南城与主城呈现跨江融合,临平城、下沙城空间上较为独立;各开发维度中,建筑强度、功能强度及效益强度热点区分布基本一致,环境响应高强度区则集聚于主副城交界处,表现出空间异质性。多维测度体系可较好表征城市开发强度,对城市规划及精细化管理具有一定的应用价值。     

A new approach to the determination of cardiac potential distributions: application to the analysis of electrode configurations

This paper presents a mathematical model and new solution technique for studying the electric potential in a slab of cardiac tissue. The model is based on the bidomain representation of cardiac tissue and also allows for the effects of fibre rotation between the epicardium and the endocardium. A detailed solution method, based on Fourier Series and a simple one-dimensional finite difference scheme, for the governing equations for electric potential in the tissue and the blood, is also presented. This method has the advantage that the potential can be calculated only at points where it is required, such as the measuring electrodes. The model is then used to study various electrode configurations which have been proposed to determine cardiac tissue conductivity parameters. Three electrode configurations are analysed in terms of electrode spacing, placement position and the effect of including fibre rotation: the usual surface four-electrode configuration; a single vertical analogue of this and a two probe configuration, which has the current electrodes on one probe and the measuring electrodes on the other, a fixed distance away. It is found that including fibre rotation has no effect on the potentials measured in the first two cases; however, in the two probe case, non-zero fibre rotation causes a significant drop in the voltage measured. This leads to the conclusion that it is necessary to include the effects of fibre rotation in any model which involves the use of multiple plunge electrodes.