Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells

The purpose of this paper is to revise the parameters of the Hodgkin-Huxley formulation for the Na+ current in ventricular myocardial cells. To this end we have assembled much of the recent voltage clamp data on cardiac preparations obtained with modern voltage clamp and patch clamp techniques. The selected activation and inactivation characteristics of the Na+ channel and other membrane parameters represent a good compromise between available experimental measurements and lead to a reasonable average representation of the cardiac Na+ membrane current. The resulting Na+ conductance changes during the action potential upstroke are much larger than in earlier models, so that the upstroke is much faster and the peak depolarization is close to the Na+ equilibrium potential. The firing threshold level is nearly constant for resting potentials in the range of -70 and -90 mV. The maximum rate of rise of the action potential displayed by the new model is quite comparable to experimental observations.     

Assessment of the maximum frequency components and digital sampling of cardiac Purkinje fiber action potentials

An investigation was made into a reasonable continuous sampling frequency for cardiac Purkinje fiber action potentials. Under the assumption that digital sampling will effectively capture frequency components up to half the sampling rate, action potential records made at 25 kHz were low-pass filtered at various cutoff frequencies. The filtered and unfiltered records were compared by calculating Vmax to determine the effects of progressive loss of high frequency components. It was determined that sampling at 13 kHz is adequate for action potentials with upstroke velocities up to 500 V/sec, and that estimation of Vmax in excess of 800 V/sec is possible.     

Estimation of time-dependent input from neuronal membrane potential

The set of firing rates of the presynaptic excitatory and inhibitory neurons constitutes the input signal to the postsynaptic neuron. Estimation of the time-varying input rates from intracellularly recorded membrane potential is investigated here. For that purpose, the membrane potential dynamics must be specified. We consider the Ornstein-Uhlenbeck stochastic process, one of the most common single-neuron models, with time-dependent mean and variance. Assuming the slow variation of these two moments, it is possible to formulate the estimation problem by using a state-space model. We develop an algorithm that estimates the paths of the mean and variance of the input current by using the empirical Bayes approach. Then the input firing rates are directly available from the moments. The proposed method is applied to three simulated data examples: constant signal, sinusoidally modulated signal, and constant signal with a jump. For the constant signal, the estimation performance of the method is comparable to that of the traditionally applied maximum likelihood method. Further, the proposed method accurately estimates both continuous and discontinuous time-variable signals. In the case of the signal with a jump, which does not satisfy the assumption of slow variability, the robustness of the method is verified. It can be concluded that the method provides reliable estimates of the total input firing rates, which are not experimentally measurable.     

A numerical reconstruction of the effects of late stimulation on a cardiac ventricular action potential.

Numerical simulations of a propagating cardiac action potential utilizing Beeler-Reuter and Drouhard-Roberge physiological routines for the membrane current have been performed. These action potentials show increases in action potential duration when subjected to strong late stimuli of either positive or negative polarity. The mechanism is the same as that reported in an earlier paper which utilized a different physiological approach: repolarizing stimuli can reset the fast sodium gates locally so that they can be retriggered by diffusive return of charge from surrounding tissue. This results in a large depolarizing transient that lengthens action potential duration.     

基于四传感器方阵的地震动目标方位角估计

针对地震动目标定位中的信号传播速度不确定性问题,提出了基于到达时间差的四传感器方阵目标方位角估计方法.从理论上推导出四传感器方阵下的目标方位角估计带边界及其最大带宽值,证明了信号传播速度与目标方位角估计之间的弱相关性.根据仿真计算深入探讨了信号传播速度和时延测量误差对目标方位角估计精度的影响.外场实验结果证明：这一方法的地震动目标方位角平均估计误差小于采用三轴地震动传感器的方法,具有一定的实用价值.     

Numerical integration in the reconstruction of cardiac action potentials using Hodgkin-Huxley-type models

A comparison between traditional numerical integration methods and a new hybrid integration method for the reconstruction of action potential activity is presented, using a mathematical model of the cardiac Purkinje fiber (MNT model). It is shown that the hybrid integration method reduces importantly the overall computation time required for solving the Hodgkin-Huxley differential equations describing membrane electrical events. To accomplish this, the particular form of the gating variable equations is exploited to reformulate the step-by-step computation. In this way, the time increment can be made much larger compared with traditional methods when the membrane potential changes slowly. A mathematical analysis of the hybrid integration method is presented also, together with a numerical verification of its performance both for the propagated and nonpropagated membrane action potential. It is shown that the local error, that is the error arising at each integration step, and the cumulative integration error are strictly controlled by the membrane potential offset. Using the MNT model, the nonpropagated cardiac Purkinje action potential can be reconstructed in real time with an accuracy of 1% for the potential and 5% for the time of occurrence of its main features. In reconstructing propagated events, the hybrid integration method allows computation time savings by a factor of 10 or more compared to accurate Runge-Kutta schemes.     

A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts

Control charts are the most popular Statistical Process Control (SPC) tools used to monitor process changes. When a control chart produces an out-of-control signal, it means that the process has changed. However, control chart signals do not indicate the real time of the process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifying the real time of the process change is known as change-point estimation problem. Most of the traditional change-point methods are based on maximum likelihood estimators (MLE) which need strict statistical assumptions. In this paper, first, we introduce clustering as a potential tool for change-point estimation. Next, we discuss the challenges of employing clustering methods for change-point estimation. Afterwards, based on the concepts of fuzzy clustering and statistical methods, we develop a novel hybrid approach which is able to effectively estimate change-points in processes with either fixed or variable sample size. Using extensive simulation studies, we also show that the proposed approach performs considerably well in all considered conditions in comparison to powerful statistical methods and popular fuzzy clustering techniques. The proposed approach can be employed for processes with either normal or non-normal distributions. It is also applicable to both phase-I and phase-II. Finally, it can estimate the true values of both in- and out-of-control states’ parameters.     

基于MLE的靶场光电经纬仪高精度定位方法研究

为解决靶场光电经纬仪现用交会定位解算模型作用范围小、与目标实际位置偏差大等问题,提高目标航迹解算精度和模型的适应范围,根据目标跟踪距离和测角误差分量关系,建立了经纬仪空间测量误差模型,优化了异面交会定位加权系数。基于最大似然估计（Maximum Likelihood Estimate,MLE）理论,提出了一种新的更高精度的定位方法,并推导了精度估算公式。详细分析了交会角度、跟踪距离和测角精度对定位误差的影响。试验证明,该方法较现用定位方法适用测量区域增加一倍以上,定位精度提高20%,更适合多测站、不等精度、远距离跟踪等工程场景,具有推广价值。     

Simulation of axonal excitability using a Spreadsheet template created in Microsoft Excel

The objective of this present study was to implement an established simulation protocol (A.M. Brown, A methodology for simulating biological systems using Microsoft Excel, Comp. Methods Prog. Biomed. 58 (1999) 181-90) to model axonal excitability. The simulation protocol involves the use of in-cell formulas directly typed into a spreadsheet and does not require any programming skills or use of the macro language. Once the initial spreadsheet template has been set up the simulations described in this paper can be executed with a few simple keystrokes. The model axon contained voltage-gated ion channels that were modeled using Hodgkin Huxley style kinetics. The basic properties of axonal excitability modeled were: (1) threshold of action potential firing, demonstrating that not only are the stimulus amplitude and duration critical in the generation of an action potential, but also the resting membrane potential; (2) refractoriness, the phenomenon of reduced excitability immediately following an action potential. The difference between the absolute refractory period, when no amount of stimulus will elicit an action potential, and relative refractory period, when an action potential may be generated by applying increased stimulus, was demonstrated with regard to the underlying state of the Na(+) and K(+) channels; (3) temporal summation, a process by which two sub-threshold stimuli can unite to elicit an action potential was shown to be due to conductance changes outlasting the first stimulus and summing with the second stimulus-induced conductance changes to drive the membrane potential past threshold; (4) anode break excitation, where membrane hyperpolarization was shown to produce an action potential by removing Na(+) channel inactivation that is present at resting membrane potential. The simulations described in this paper provide insights into mechanisms of axonal excitation that can be carried out by following an easily understood protocol.     

Change of short-term memory effect in acute ischemic ventricular myocardium: A computational study

The ionic mechanism of change in short-term memory (STM) during acute myocardial ischemia has not been well understood. In this paper, an advanced guinea pig ventricular model developed by Luo and Rudy was used to investigate STM property of ischemic ventricular myocardium. STM response was calculated by testing the time to reach steady-state action potential duration (APD) after an abrupt shortening of basic cycling length (BCL) in the pacing protocol. Electrical restitution curves (RCs), which can simultaneously visualize multiple aspects of APD restitution and STM, were obtained from dynamic and local S1S2 restitution portrait (RP), which consist of a longer interval stimulus (S1) and a shorter interval stimulus (S2). The angle between dynamic RC and local S1S2 RC reflects the amount of STM. Our results indicated that compared with control (normal) condition, time constant of STM response in the ischemic condition decreased significantly. Meanwhile the angle which reflects STM amount is less in ischemic model than that in control model. By tracking the effect of ischemia on intracellular ion concentration and membrane currents, we declared that changes in membrane currents caused by ischemia exert subtle influences on STM; it is only the decline of intracellular calcium concentration that give rise to the most decrement of STM.     

基于Thevenin模型和自适应卡尔曼的SOC估算研究

精确的荷电状态(SOC)值在电池的应用开发中具有重要的意义.选择合适的滤波算法是精确估算的前提.由于扩展卡尔曼滤波(EKF)中噪声的给定值与实际工况下噪声的统计特性不符,导致估算精度低.为提高SOC估算精度,构建能准确反映锂电池工作特性的Thevenin电路模型.在此基础上,构建状态方程和观测方程,提出自适应卡尔曼滤波...     

A windows software for simulation of the membrane excitation in nerve and skeletal muscle fiber.

A windows 95/98 software program for simulating membrane excitation in nerve and skeletal muscle fiber has been developed. This program simulates (1) the action potentials of the nerve under two conditions (space clamped conditions and conducting conditions), (2) the membrane currents of the nerve under voltage clamped conditions, and (3) the propagated action potentials of skeletal muscle fiber. Since users can utilize quadruple precision in the simulation of propagated action potentials, such simulation can be done for a long period (60 ms in skeletal muscle at 2 degrees C). In addition, users can change the conditions such as the capacitance of the membrane, the maximum conductance of the channel, etc., arbitrarily without quitting the program. It is also possible to easily modify the time and the voltage dependence of the gate particles in order to confirm the effects of various changes on the action potential or the membrane current. This program also has an analysis mode in which the current-voltage relationship of a channel can be measured automatically.     

Improved Pose Estimation for Mobile Robots by Fusion of Odometry Data and Environment Map

This paper proposes a new approach for calibration of dead reckoning process. Using the well-known UMBmark (University of Michigan Benchmark) is not sufficient for a desirable calibration of dead reckoning. Besides, existing calibration methods, usually require explicit measurement of actual motion of the robot. Some recent methods, use the smart encoder trailer or long range finder sensors such as ultrasonic or laser range finders for automatic calibration. Manual measurement is necessary in the case of the robots that are not equipped with long range detectors or such smart encoder trailer. Our proposed approach, uses an environment map that is created by fusion of proximity data, in order to calibrate the odometry error automatically. In the new approach, the systematic part of the error is adaptively estimated and compensated by an efficient and incremental maximum likelihood algorithm. Actually, environment map data are fused with the odometry and current sensory data in order to acquire the maximum likelihood estimation. The advantages of the proposed approach are demonstrated in some experiments with Khepera robot. It is shown that the amount of pose estimation error is reduced by a percentage of more than 80%.     

Full and conditional likelihood approaches for hazard change-point estimation with truncated and censored data

Hazard function plays an important role in reliability and survival analysis. In some real life applications, abrupt changes in the hazard function may be observed and it is of interest to detect the location and the size of the change. Hazard models with a change-point are considered when the observations are subject to random left truncation and right censoring. For a piecewise constant hazard function with a single change-point, two estimation methods based on the maximum likelihood ideas are considered. The first method assumes parametric families of distributions for the censoring and truncation variables, whereas the second one is based on conditional likelihood approaches. A simulation study is carried out to illustrate the performances of the proposed estimators. The results indicate that the fully parametric method performs better especially for estimating the size of the change, however the difference between the two methods vanish as the sample size increases. It is also observed that the full likelihood approach is not robust to model misspecification.     

A finite element approach for analyzing the effect of cushion type and thickness on pressure ulcer

Immobilization or continuous sitting with a constant posture for a long time in office environment causes sub-dermal tissue damage. Tissue damage occurs because of continuous prolonged compression of buttock soft tissue under body weight. It is treated as the end result of cell death or tissue deformation which ultimately gives rise to pressure ulcer. Although the sub-dermal tissue refers to the tissue beneath the skin, it is the tissue just below the bony portion undergoes maximum deformation because the muscle endures a continuous high stress. In this work, a simple but practical numerical approach has been proposed to estimate the maximum stress beneath the bony structure (ischial tuberosity). The model is validated with experimental data from the literature. Effect of properties of cushion material, loading angle and thickness of cushion has been analyzed. The cushion properties and thickness that can reduce maximum stress at ischial tuberosity have been demonstrated. The effect of sitting posture on maximum stress at ischial tuberosity has also been shown.     

A set theoretic approach for time-to-contact estimation in dynamic vision

This paper deals with the estimation of the time-to-contact in dynamic vision. It is well known that differential invariants of the image velocity field can be used to characterize the shape changes of objects in the scene, due to relative motion between the observer and the scene. Under the hypothesis of constant velocity along the optical axis, the time-to-contact turns out to be a function of the area enclosed by the object contour and its time derivative.In the paper, a novel approach based on set membership estimation theory is proposed to estimate the variables involved in the computation of the time-to-contact. Both errors in the motion model and image measurement noise are described as unknown-but-bounded disturbances, without requiring any statistical assumption. The proposed technique allows for the computation of guaranteed bounds on the time-to-contact estimates in finite time, a crucial issue in all problems where a robust evaluation of the time-to-contact is in order.     

Genetic CONDENSATION for motion tracking

Tracking serves as a means to prepare data for pose estimation and action recognition. The CONDENSATION algorithm is a conditional density propagation method for motion tracking. This algorithm combines factored sampling with learned dynamic models to propagate an entire probability distributes for object position and shape over time. It can accomplish highly robust tracking of object motion. However, it usually requires a large number of samples to ensure a fair maximum likelihood estimation of the current state. In this paper, we use the mutation and crossover operators of the genetic algorithm to find appropriate samples. With this approach, we are able to improve robustness, accuracy and flexibility in CONDENSATION for visual tracking.     

Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory

This paper combines polynomial chaos theory with maximum likelihood estimation for a novel approach to recursive parameter estimation in state-space systems. A simulation study compares the proposed approach with the extended Kalman filter to estimate the value of an unknown damping coefficient of a nonlinear Van der Pol oscillator. The results of the simulation study suggest that the proposed polynomial chaos estimator gives comparable results to the filtering method but may be less sensitive to user-defined tuning parameters. Because this recursive estimator is applicable to linear and nonlinear dynamic systems, the authors portend that this novel formulation will be useful for a broad range of estimation problems.     

A robust estimator for the tail index of Pareto-type distributions

In extreme value statistics, the extreme value index is a well-known parameter to measure the tail heaviness of a distribution. Pareto-type distributions, with strictly positive extreme value index (or tail index) are considered. The most prominent extreme value methods are constructed on efficient maximum likelihood estimators based on specific parametric models which are fitted to excesses over large thresholds. Maximum likelihood estimators however are often not very robust, which makes them sensitive to few particular observations. Even in extreme value statistics, where the most extreme data usually receive most attention, this can constitute a serious problem. The problem is illustrated on a real data set from geopedology, in which a few abnormal soil measurements highly influence the estimates of the tail index. In order to overcome this problem, a robust estimator of the tail index is proposed, by combining a refinement of the Pareto approximation for the conditional distribution of relative excesses over a large threshold with an integrated squared error approach on partial density component estimation. It is shown that the influence function of this newly proposed estimator is bounded and through several simulations it is illustrated that it performs reasonably well at contaminated as well as uncontaminated data.     

A robust estimator for the tail index of Pareto-type distributions

In extreme value statistics, the extreme value index is a well-known parameter to measure the tail heaviness of a distribution. Pareto-type distributions, with strictly positive extreme value index (or tail index) are considered. The most prominent extreme value methods are constructed on efficient maximum likelihood estimators based on specific parametric models which are fitted to excesses over large thresholds. Maximum likelihood estimators however are often not very robust, which makes them sensitive to few particular observations. Even in extreme value statistics, where the most extreme data usually receive most attention, this can constitute a serious problem. The problem is illustrated on a real data set from geopedology, in which a few abnormal soil measurements highly influence the estimates of the tail index. In order to overcome this problem, a robust estimator of the tail index is proposed, by combining a refinement of the Pareto approximation for the conditional distribution of relative excesses over a large threshold with an integrated squared error approach on partial density component estimation. It is shown that the influence function of this newly proposed estimator is bounded and through several simulations it is illustrated that it performs reasonably well at contaminated as well as uncontaminated data.