On the possibility for computing the transmembrane potential in the heart with a one shot method: an inverse problem

We analyze the possibility for using body surface potential maps (BSPMs), a priori information about the voltage distribution in the heart and the bidomain equations to compute the transmembrane potential throughout the myocardium. Our approach is defined in terms of an inverse problem for elliptic partial differential equations (PDEs). More precisely, we formulate it in terms of an output least squares framework in which a goal functional is minimized subject to suitable PDE constraints. The problem is highly unstable and, even under optimal recording conditions, it does not have a unique solution. We propose a methodology for stabilizing and enforcing uniqueness for this inverse problem. Moreover, a fully implicit method for solving the involved minimization problem is presented. In other words, we show how one may solve it in terms of a system consisting of three linear elliptic PDEs, i.e. we derive a so-called one shot method (also commonly referred to as an all-at-once method). Finally, our theoretical findings are illuminated by a series of numerical experiments. These examples indicate that, in the presence of regional ischemia, it might be possible to approximately recover the transmembrane potential during the resting and plateau phases of the heart cycle. This is probably due to the fact that rather accurate a priori information is available during these time intervals. The problem of computing the transmembrane potential at an arbitrary time instance during a heart beat is still an open problem.     

A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes

A generalized finite difference (GFD) method is presented that can be used to solve the bi-domain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bi-domain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bi-domain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bi-domain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bi-domain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles.     

Effects of changes in extracellular pH and potassium concentration on Kv1.3 inactivation

The Kv1.3 channel inactivates via the P/C-type mechanism, which is influenced by a histidine residue in the pore region (H399, equivalent of Shaker 449). Previously we showed that the electric field of the protonated histidines at low extracellular pH (pHe) creates a potential barrier for K+ ions just outside the pore that hinders their exit from the binding site controlling inactivation (control site) thereby slowing inactivation kinetics. Here we examined the effects of extracellular potassium [K+]e and pHe on the rate of inactivation of Kv1.3 using whole-cell patch-clamp. We found that in 150 mM [K+]e inactivation was accelerated upon switching to pHe 5.5 as opposed to the slowing at 5 mM [K+]e. The transition from slowing to acceleration occurred at 40 mM [K+]e, whereas this "turning point" was at 20 mM [K+]e for inward currents. The rate of entry of Ba(2+) ions from the extracellular space to the control site was significantly slowed by low pHe in wild-type hKv1.3, but it was insensitive to pH(e) in H399K and H399L mutants. Based on these observations we expanded our model and propose that the potential barrier created by the protonated histidines impedes the passage of K+ ions between the extracellular medium and the control site in both directions and the effect on inactivation rate (acceleration or slowing) depends on the relative contribution of filling from the extracellular and intracellular sides.     

Ion concentration dynamics as a mechanism for neuronal bursting

We describe a simple conductance-based model neuron that includes intra- and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.     

The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: A computational study

Experimental evidences point out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular ions) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K⁺]_o and a decrease of extracellular calcium concentration [Ca²⁺]_o which raises the neuronal excitability. However, whether the high [K⁺]_o triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K⁺]_o and zero [Ca²⁺]_o were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na⁺-K⁺ pump, ion diffusion and glial buffering. Within these conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na⁺−K⁺ pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K⁺ dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K⁺]_o, transiting to an elevated state of neuronal excitability. Effects of high [K⁺]_o are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K⁺]_o creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K⁺]_o by outward K⁺ flow depresses K⁺ currents in a positive feedback way. At the last stage, due to the depression of K⁺ currents, the Na⁺-K⁺ pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K⁺]_o dynamics may play a fundamental role in these abnormal oscillatory patterns.     

An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso

In this paper we present a numerical method for the bidomain model, which describes the electrical activity in the heart. The model consists of two partial differential equations (PDEs), which are coupled to systems of ordinary differential equations (ODEs) describing electrochemical reactions in the cardiac cells. Many applications require coupling these equations to a third PDE, describing the electrical fields in the torso surrounding the heart. The resulting system is challenging to solve numerically, because of its complexity and very strict resolution requirements in time and space. We propose a method based on operator splitting and a fully coupled discretization of the three PDEs. Numerical experiments show that for simple simulation cases and fine discretizations, the algorithm is second-order accurate in space and time.     

Observations on the relationship between the extracellular changes of taurine and glutamate during cortical spreading depression, during ischemia, and within the area surrounding a thrombotic infarct

Summary. Taurine and glutamate were monitored by microdialysis technique during various cerebral insults: a. Application of K⁺ triggered a cortical spreading depression (CSD). Taurine and glutamate increased concomitantly but recovery of glutamate was faster than that of taurine. b. Application of NMDA induced also CSD but only taurine increased. c. Induction of an infarct triggered repetitive CSDs. Taurine increased rapidly whereas glutamate rose slowly starting with some delay. d. After induction of ischemia, taurine and glutamate increased after onset of depolarisation. The increase of glutamate occurred late after a small, transient increase in parallel with the depolarisation. These data suggest a close functional relationship between the changes of both amino acids. Therefore, they should be monitored together especially in clinical settings: during excitation, only taurine will increase; during overexcitation, taurine will also increase but to a higher maximum followed by a moderate rise of glutamate; after energy failure, taurine will accumulate to its highest level followed by a continuous rise of glutamate. Received January 25, 2000/Accepted January 31, 2000     

Functional evidence for a supramolecular structure for the Streptomyces lividans potassium channel KcsA

Here we present functional evidence for involvement of poly-(R)-3-hydroxybutyrate (PHB) and inorganic polyphosphate (polyP) in ion conduction and selection at the intracellular side of the Streptomyces lividans potassium channel, KcsA. At < or = 25 degrees C, KcsA forms channels in planar bilayers that display signal characteristics of PHB/polyP channels at the intracellular side; i.e., a preference for divalent Mg(2+) cations at pH 7.2, and a preference for monovalent K+ cations at pH 6.8. Between 25 and 26 degrees C, KcsA undergoes a transition to a new conformation in which the channel exhibits high selectivity for K+, regardless of solution pH. This suggests that basic residues of the C-terminal polypeptides have moved closer to the polyP end unit, reducing its negative charge. The data support a supramolecular structure for KcsA in which influx of ions is prevented by the selectivity pore, whereas efflux of K+ is governed by a conductive core of PHB/polyP in partnership with the C-terminal polypeptide strands.     

Isolating the segment of the mitochondrial electron transport chain responsible for mitochondrial damage during cardiac ischemia

Ischemia damages the mitochondrial electron transport chain (ETC), mediated in part by damage generated by the mitochondria themselves. Mitochondrial damage resulting from ischemia, in turn, leads to cardiac injury during reperfusion. The goal of the present study was to localize the segment of the ETC that produces the ischemic mitochondrial damage. We tested if blockade of the proximal ETC at complex I differed from blockade distal in the chain at cytochrome oxidase. Isolated rabbit hearts were perfused for 15 min followed by 30 min stop-flow ischemia at 37 °C. Amobarbital (2.5 mM) or azide (5 mM) was used to block proximal (complex I) or distal (cytochrome oxidase) sites in the ETC. Time control hearts were buffer-perfused for 45 min. Subsarcolemmal mitochondria (SSM) and interfibrillar mitochondria (IFM) were isolated. Ischemia decreased cytochrome c content in SSM but not in IFM compared to time control. Blockade of electron transport at complex I preserved the cytochrome c content in SSM. In contrast, blockade of electron transport at cytochrome oxidase with azide did not retain cytochrome c in SSM during ischemia. Since blockade of electron transport at complex III also prevented cytochrome c loss during ischemia, the specific site that elicits mitochondrial damage during ischemia is likely located in the segment between complex III and cytochrome oxidase.     

Estimating a predator-prey dynamical model with the parameter cascades method

Summary .   Ordinary differential equations (ODEs) are widely used in ecology to describe the dynamical behavior of systems of interacting populations. However, systems of ODEs rarely provide quantitative solutions that are close to real field observations or experimental data because natural systems are subject to environmental and demographic noise and ecologists are often uncertain about the correct parameterization. In this article we introduce "parameter cascades" as an improved method to estimate ODE parameters such that the corresponding ODE solutions fit the real data well. This method is based on the modified penalized smoothing with the penalty defined by ODEs and a generalization of profiled estimation, which leads to fast estimation and good precision for ODE parameters from noisy data. This method is applied to a set of ODEs originally developed to describe an experimental predator–prey system that undergoes oscillatory dynamics. The new parameterization considerably improves the fit of the ODE model to the experimental data sets. At the same time, our method reveals that important structural assumptions that underlie the original ODE model are essentially correct. The mathematical formulations of the two nonlinear interaction terms (functional responses) that link the ODEs in the predator–prey model are validated by estimating the functional responses nonparametrically from the real data. We suggest two major applications of "parameter cascades" to ecological modeling: It can be used to estimate parameters when original data are noisy, missing, or when no reliable priori estimates are available; it can help to validate the structural soundness of the mathematical modeling approach.     

NIR spectroscopic imaging to map hemoglobin + myoglobin oxygenation,their concentration and optical pathlength across a beating pig heart during surgery

The purpose of this paper is to demonstrate that near‐infrared (NIR) spectroscopic imaging can provide spatial distribution (maps) of the absolute concentration of hemoglobin + myoglobin, oxygen saturation parameter and optical pathlength, reporting on the biochemico‐physiological status of a beating heart in vivo. The method is based on processing the NIR spectroscopic images employing a first‐derivative approach. Blood‐pressure‐controlled gating compensated the effect of heart motion on the imaging. All the maps are available simultaneously and noninvasively at a spatial resolution in the submillimeter range and can be obtained in a couple of minutes. The equipment has no mechanical contact with the tissue, thereby leaving the heart unaffected during the measurement. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A model for proton and potassium co-transport during the uptake of glutamine and sucrose by tomato internode disks

Internode disks of tomato (Lycopersicon esculentum cv. Moneymaker) were shaken in glutamine and sucrose solutions. At low external pH (<±5.5), the uptake of these substances was accompanied with K⁺ efflux, at high pH (>±5.5) with K⁺ influx. Low concentrations of external K⁺ (2 mmol l^-1) stimulated the uptake of glutamine, which was strongly inhibited by the supply of high K⁺ concentrations (20 mmol l^-1). The effect of K⁺ was particularly pronounced at high pH-values. Addition of CCCP in light reduced the uptake of glutamine to the same level as in the dark, and stopped the K⁺ fluxes which coincided with the uptake. A model is presented wherein the movements of K⁺ across the membrane are related to co-transport, depending on the membrane potential and the Nernst potential of K⁺.Abbreviation CCCP carbonylcyanide-m-chlorophenylhydrazone     

Assessment of the cryoprotectant concentration inside a bulky organ for cryopreservation using X-ray computed tomography

Cryoprotection of bulky organs is crucial for their storage and for subsequent transplantation. In this work we demonstrate the capability of the X-ray computed tomography (CT) as a non-invasive method to measure the cryoprotectant (cpa) concentration inside a tissue or an organ, specifically for the case of dymethil sulfoxide (Me₂SO). It is remarkable that the use of Me₂SO has been leader in techniques of cells and tissues cryopreservation. Although CT technologies are mainly based in density differences, and many cpas are alcohols with densities similar to water, the use of very low energies as acceleration voltage (∼70 kV) and the sulfur atom in the molecule of Me₂SO makes possible the visualization of this cpa inside tissues. As result we obtain a CT signal proportional to the Me₂SO concentration with a spatial resolution up to 50 μm in the case of our device.     

鼎湖山三种主要林型水文学过程中总有机碳浓度对比

为了解碳在森林内部以及群落演替过程中的转运动态 ,对鼎湖山 3种主要林型 (马尾松林 ,马尾松针阔混交林和季风常绿阔叶林 )森林水文学过程中总有机碳 (total organic carbon,TOC)浓度进行了一个雨季的观测 ,结果发现 :(1)穿透水中 TOC浓度相对大气降水中 TOC浓度的增量为 :季风常绿阔叶林 >马尾松针阔混交林 1>马尾松针阔混交林 2 >马尾松林 ;(2 )树干茎流平均 TOC浓度为 :马尾松林 >马尾松针阔混交林 2 >马尾松针阔混交林 1>季风常绿阔叶林 ;(3)各林内土壤水 TOC浓度差异不明显 ,但根系层 (2 5～ 30 cm)土壤水 TOC浓度均大于母质层 (5 0～ 80 cm) TOC浓度 ;(4 )马尾松林的溪水具有较高的 TOC浓度和较大的月际波动 ;(5 )总体上 ,整个森林水文学过程中 ,3种林型 TOC浓度变化趋势相似 ,均为 :树干茎流 >穿透水 >根系层土壤水 >母质层土壤水 >溪水 ,但变化幅度不同 :马尾松林的变化幅度最大 ,季风林的最小 ,而两个混交林居中。这表明 ,(1)森林演替过程中 ,林冠层结构、树种构成等的改变可能引起森林水文学过程中 TOC浓度的变化 ;(2 )森林水文学过程转运的碳主要储存在森林内部 ;(3)成熟森林的抗干扰能力高于先锋群落     

5-Dodecanoylaminofluorescein as a probe for the determination of critical micelle concentration of detergents using fluorescence anisotropy

A method for determining the critical micelle concentration (CMC) of various detergents based on fluorescence polarization (anisotropy) of the lipophilic probe 5-dodecanoylaminofluorescein is presented. Nonionic, cationic, anionic, and steroid-based detergents can all be evaluated by this method and the determined CMC values of selected detergents agree well with those reported in the literature. In addition, we report the CMC of domiphen bromide, whose CMC value has not previously been described. In the case of ionic detergents, the method described is particularly sensitive at discerning changes in the CMC with increasing ionic strength of the medium and can discriminate detergent CMCs in 5 mM versus 25 mM buffering components. The described fluorescence polarization technique allows very low (submicromolar) concentrations of probe to be employed, thus minimizing the perturbation of micelle formation by 5-dodecanoylaminofluorescein insertion.     

Fluctuations in concentration of two potyviruses in garlic during the growing period and sampling conditions for reliable detection by ELISA

To optimise sampling conditions for the detection by ELISA of Onion yellow dwarf virus (OYDV) and Leek yellow stripe virus (LYSV), the most important viral pathogens of garlic worldwide, relative virus concentrations were determined during the growing period and in different leaf parts by DAS‐ELISA. Both viruses were found to have uneven distributions in garlic plants, with the tips of the two latest fully developed leaves showing the highest concentrations and the oldest leaves the lowest concentrations. The tips of the youngest leaves were found to have higher virus concentrations than their middle and basal sections. In the older leaves, viruses were distributed more uniformly in the three leaf sections. In the oldest leaves virus levels in the leaf tips were significantly decreased. The concentrations of OYDV and LYSV increased until March, whereas later on they decreased. During storage of leaf samples at 6°C for 15 days, a loss was found of both virus antigens of more than 80%, and during 109 days of storage at ?30°C a loss of more than 90% was found.     

Preliminary results of a new approach for three-dimensional reconstruction of Dynamic AngioThermography (DATG) images based on the inversion of heat equation

Dynamic AngioThermography (DATG) is a contact-plate technique capable of producing a digital representation of breast vascularity. The inception and growth of a tumor are associated with neoangenesis, which may result in a demonstrable alteration in the regional blood flow, while in normal health conditions the vascularity remains unchanged throughout life. DATG, if included in the clinical evaluation for breast cancer, could potentially improve the accuracy of the diagnosis of this disease.Conventional DATG is limited, however, in that it is a projection (i.e. two-dimensional) imaging technique that does not provide any information on the depth and its effect on the pattern of the perfusion revealed by this technique. In fact, the blood pattern is detected by projecting temperature signals on the plate, thus acquiring a digital two-dimensional image.In this article we propose a new approach for extracting information on depth through the inversion of the Fourier heat equation. The idea is to extract the information along the third axis while acquiring and analyzing the temporal sequence during the process of image formation. The method implemented has been tested on a dedicated “electric phantom” and in one in vivo experiment.In spite of the limits of these preliminary tests, the experimental results have shown that this method makes it possible to obtain a 3D representation of the vascularity. Although it appears to be promising, further validation and characterization of our technique are required.     

Examination of the method for measuring soil respiration in cultivated land: Effect of carbon dioxide concentration on soil respiration

An acceleration of soil respiration with decreasing CO₂ concentration was suggested in the field measurements. The result supporrs that obtained in laboratory experiments in our previous study. The CO₂ concentrations in a chamber of the alkali absorption method (the AA-method) were about 150–250 parts/10⁶ lower than that in the atmosphere (about 350 parts/10⁶), while those observed in the open-flow IRGA method (the OF-method) were nearly equal to the soil surface CO₂ levels. The AA-method at such low CO₂ levels in the chamber appears to overestimate the soil respiration. Our results showed that the rates obtained by the AA-method were about twice as large as those by the OF-method in field and laboratory measurements. This finding has important consequences with respect to the validity of the existing data obtained by the AA-method and the estimation of changes in the terrestrial carbon flow with elevated CO₂     

基于CFTR的胞浆内第二信使cAMP检测方法的建立*

目的: 建立一种基于CFTR可敏感检测胞浆内第二信使cAMP的检测方法。方法: 构建CFTR和YFP-H148Q/I152L真核表达载体,应用脂质体转染法构建共表达CFTR和YFP-H148Q/I152L的FRT细胞,倒置荧光显微镜观察其表达情况,流式细胞仪检测细胞纯度;荧光淬灭动力学实验验证细胞模型的有效性;荧光淬灭动力学实验验证细胞模型可筛选CFTR调节剂;放射免疫法检测加入CFTR激活剂后细胞内的cAMP浓度。结果: 倒置荧光显微镜下观察到CFTR表达在细胞膜上,YFP-H148Q/I152L表达于胞浆中;成功构建共表达CFTR和YFP-H148Q/I152L的FRT细胞模型;荧光变化斜率值与CFTR调节剂浓度成剂量依赖关系,该模型可筛选CFTR调节剂;荧光变化斜率值可反映胞浆内cAMP浓度,该模型可敏感检测胞浆内cAMP浓度。结论: 此细胞模型可以高效敏感检测胞浆内第二信使cAMP浓度,为cAMP信号相关靶点的研究提供一种简便快捷的方法。     

Rubidium as a probe for function and transport of potassium in the yeast Candida utilis NCYC 321, grown in chemostat culture

Attempts to grow the yeast Candida utilis in continuous culture, using media in which all the potassium had been replaced by other monovalent cations, revealed that neither lithium, sodium, caesium nor ammonium ions could functionally substitute for potassium. However, potassium could be effectively replaced by rubidium which gave (on a molar basis, and under conditions where cation availability limited growth) the same yield of cells as did potassium.Comparison of potassium- and rubidium-limited cultures showed them to be virtually identical in all the measured parameters, with the single exception of the maximum growth rate value which was considerably decreased in the rubidium-containing culture (0.35 h^-1 as compared with 0.55 h^-1).When, with variously-limited chemostat cultures, both potassium and rubidium were supplied in equimolar amounts, these ions were taken up by the cells in a ratio that varied with both the growth rate and the nature of the growth limitation. With glucose-, phosphate- or magnesium-limited cultures, the molar ratio K⁺:Rb⁺ was 1:0.6 (at D=0.1 h^-1) and 1:0.17 (at D=0.5 h^-1). In contrast, ammonia-limited cultures took up increased amounts of rubidium when growing at a low rate such that the ratio was 1:1.2, at D=0.1 h^-1, though still 1:0.17 at the higher growth rate value (D=0.5 h^-1).From a comparison of glucose- and ammonialimited cultures growing first with an equimolar mixture of potassium and rubidium, and then with rubidium alone, it was noted that the yield on oxygen was significantly decreased when potassium was absent.These results are discussed in relation to the transport and possible functions of monovalent cations in micro-organisms. It was concluded that, on the basis of these experiments, some objections could be raised against estimation of potassium transport rates by means of the tracer ⁸⁶Rb.