A procedure to determine equilibrium postural configurations for arbitrary locations of the feet

This research was directed toward predicting postural equilibrium configurations in normal humans for asymmetric locations of the feet. The objective of the study was to identify trends in the variation of the location of ground center of pressure (COP) with increasing levels of asymmetry in the foot placement. The procedure developed here minimized the muscular effort (active torques) in the lower extremities while maximizing postural stability margins for given foot locations. Minimizing muscular effort led to fully extended knees, and maximal stability margin led to the COP moving toward the rear foot in asymmetric stance. A combined analytical-numerical optimization scheme was used to avoid singularities that can arise due to the fact that at equilibrium postural configurations, the torso lies at or near the workspace boundary of the lower extremities. Experiments were conducted and the results obtained were in keeping with the model predictions. This basic understanding of asymmetric stance is important for studying asymmetric postural mechanics in the presence of external disturbances, and for extending the results from normal subjects to humans at both ends of the life span.     

The electronic spreadsheet as a general-purpose programming tool

Electronic spreadsheets computerise the traditional layout ofany tabulation or complex calculation done with pencil, paperand calculator. They therefore have great potential in aidingroutine calculations which might be done by these means or witha small BASIC computer program. Their simple structure and strongaffinity with traditional methods make them particularly suitablefor those who have not yet mastered the art of programming.However, a necessarily brief review of their application toscience and technology demonstrates that this potential is notbeing realised in comparison with their widespread usage inthe business world. The application of both Multiplan and Visicalcrunning respectively on the Macintosh and the Apple He microcomputersin four types of calculation is demonstrated: tabulation, curve–fittingand statistics, simulation, and numerical approximation. Advantagesare found in the concurrent display of data and results, theease of correction or modification of data and the escape fromtraditional linear programming methods. The spreadsheet formatimposes its own constraints. It is not so flexible as BASIC,it demands more memory and may have a slower execution timethan a program written in a high–level language, and itis more difficult to produce graphical output.     

A basic biophysical model for bursting neurons

Presented here is a basic biophysical cell model for bursting, an extension of our previous model (Av-Ron et al. 1991) for excitability and oscillations. By changing a limited set of model parameters, one can describe different patterns of bursting behavior in terms of the burst cycle, the durations of oscillation and quiescence, and firing frequency.     

A model for repetitive firing in neurons

This paper describes a model for the generation of repetitive firing patterns in single neurons to be used as a module in large-scale network simulation studies. The model is based on the combination of extended versions of Hill's model for accomodation and of Kernell's model for adaptation. Both digital computer and electronic circuit realizations of the model are presented. The model is shown to produce strength-duration curves for accomodation which are compatible with available data from real neurons. Both “high ceiling” and “low ceiling” cell types can be matched by adjusting parameters in the model. An equation relating steady-state firing rate to amplitude of applied steady current is presented which includes the accumulation of potassium conductance changes with repetitive firing. The occurence of phasic and tonic responses to step stimulation is mapped in the parameter space of the model. Several representative response patterns to irregular inputs are presented.     

A volumetric model for growth of arterial walls with arbitrary geometry and loads

Stress and deformation in arterial wall tissue are factors which may influence significantly its response and evolution. In this work we develop models based on nonlinear elasticity and finite element numerical solutions for the mechanical behaviour and the remodelling of the soft tissue of arteries, including anisotropy induced by the presence of collagen fibres. Remodelling and growth in particular constitute important features in order to interpret stenosis and atherosclerosis. The main object of this work is to model accurately volumetric growth, induced by fluid shear stress in the intima and local wall stress in arteries with patient-specific geometry and loads. The model is implemented in a nonlinear finite element setting which may be applied to realistic 3D geometries obtained from in vivo measurements. The capabilities of this method are demonstrated in several examples. Firstly a stenotic process on an idealised geometry induced by a non-uniform shear stress distribution is considered. Following the growth of a right coronary artery from an in vivo reconstructed geometry is presented. Finally, experimental measurements for growth under hypertension for rat carotid arteries are modelled.     

A generalized tapering equivalent cable model for dendritic neurons

A mathematical model has been developed which collapses a dendritic neuron of complex geometry into a single electrotonically tapering equivalent cable. The modified cable equation governing the transient distribution of subthreshold membrane potential in a branching tree is transformed, becoming amenable to analytic solution. This transformation results in a Riccati differential equation whose six solutions (expressed in terms of elementary functions) control the amount and degree of taper found in the equivalent cable model. To illustrate the theory, an analytic solution (in series form) of the modified cable equation is obtained for a voltage-clamp present at the soma of a quadratically tapering equivalent cable whose distal end is sealed.     

A model for generalization and specification by single neurons

A rule for environmentally dependent modification of the neuronal state is examined. Under the rule, the neuron selects a trigger feature that matches either a particular pattern in the stimulus set, or the most common pattern component, depending on a certain parameter. Thus a neuron may evolve to respond to its stimulus environment in one of two capacities, namely specification or generalization. Neurons of the former variety are labelled S-cells; and those of the latter, G-cells. In the model, synaptic modification is modulated by two postsynaptic mechanisms which act antagonistically to strengthen or weaken the synaptic connectivities. The functional dependence of these mechanisms on the postsynaptic activity is shown to determine whether the neuron acts as an S-cell or a G-cell. A circuit is proposed for a module that consists of a G-cell and several S-cells sharing a common set of inputs. By inhibiting the G-cells, the S-cell acts as a contrast-enhancing element, increasing their specificities for individual patterns in the stimulus set. The output from the module is a recoded representation of the environment with respect to its general and distinctive features.This work was supported in part by United States Office of Naval Research Contract N00014-81-K-0136     

RF-cell: A model for populations of randomly interconnected neurons

This paper is concerned with a population of neurons with dense random interconnections, in which the stimulations between neurons are independent of their distance apart. This study is conducted from the viewpoint of the General System Theory. Proposed and used for the first time in studies on the above subject is a new concept referred to as the ‘historical report’ of the mentioned population. It will be shown that the population exhibits cyclic modes of behaviour which are dependent on its structure and historical report and which in the phase space correspond to cycles of hysteresis. A simple model in discrete time is developed and demonstrates, by the help of a computer study, the existence of the cycles of hysteresis.     

A cable model for coupled neurons with somatic gap junctions

A cable model is presented for a pair of electrotonically coupled neurons to investigate the spatial effects of soma-somatic gap junctions. The model extends that of Poznanski et al.(1995) in which each neuron is represented by a tapered equivalent cable attached to an isopotential soma with the two somas being electrically coupled. The model is posed generally, so that both active and passive properties can be considered. In the active case a system of nonlinear integral equations is derived for the voltage, whilst in the passive case these have an exact solution that also holds for inputs modelled as synaptic reversal potentials. Analytical and numerical methods are used to examine the sensitivity of the soma potentials (in particular) to the coupling resistance.     

A general-purpose system for characterizing medically important bacteria to genus level

A computer program and accompanying data matrix have been prepared for bacteria of medical interest, to assist the assignment of an unidentified bacterium to the most likely genus. The results on a set of relatively simple tests are entered. The program prints the more likely genera, followed by a list of diagnostic tables in Cowan & Steel (1974) and Buchanan & Gibbons (1974). Where available, identification matrices for further computer-assisted study, are presented. This program may be of particular help in laboratories where a wide range of bacteria have to be identified.     

A system model for investigating passive electrical properties of neurons.

Passive membrane properties of neurons, characterized by a linear voltage response to constant current stimulation, were investigated by busing a system model approach. This approach utilizes the derived expression for the input impedance of a network, which simulates the passive properties of neurons, to correlate measured intracellular recordings with the response of network models. In this study, the input impedances of different network configurations and of dentate granule neurons, were derived as a function of the network elements and were validated with computer simulations. The parameters of the system model, which are the values of the network elements, were estimated using an optimization strategy. The system model provides for better estimation of the network elements than the previously described signal model, due to its explicit nature. In contrast, the signal model is an implicit function of the network elements which requires intermediate steps to estimate some of the passive properties.     

A unified model for two modes of bursting in GnRH neurons

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca²⁺ current I _s, and the Ca²⁺ -activated K⁺ current I _KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.     

A simple stochastic model of spatially complex neurons

A method for studying the coding properties of a multicompartmental integrate-and-fire neuron of arbitrary geometry is presented. Depolarization at each compartment evolves like a leaky integrator with an after-firing reset imposed only at the trigger zone. The frequency of firing at the steady-state regime is related to the properties of the multidimensional input. The decreasing variability of subthreshold depolarization from the dendritic tree to the trigger zone is shown for an input that is corrupted by a white noise. The role of a Poissonian noise is also investigated. The proposed method gives an estimate of the mean interspike interval that can be used to study the input output transfer function of the system. Both types of the stochastic inputs result in broadening the transfer function with respect to the deterministic case.     

Threshold model for clustered firing of neurons

Two probabilistic threshold models for burst activity of cortical neurons are proposed. In model I every input impulse increases the summed effect of previous input impulses by one unit. The decay of the summed effect takes place in discrete steps of one unit. A response occurs on arrival of an input impulse, when a threshold value is attained.Although after a response the summed effect is not reset to zero, it cannot exceed the threshold either. The distribution of intervals can be resolved in two components, one for long and one for short intervals. In model II intervals of the short component are terminated by a multiple response instead of one response.     

A model of oscillation generation by molluscan neurons

A model describing slow oscillations of membrane potential in molluscan neurons is suggested. It is based on the view that the depolarization phase is due to the slow calcium current, whereas the hyperpolarization phase is due to the potassium current activated by intracellular Ca ions. It is shown that depending on values of the parameters of the model there are three possible types of electrical activity of the neurons: stable membrane hyperpolarization up to the resting potential which is between ?49 and ?53 mV; slow oscillations of membrane potential from ?30 to ?60 mV, with a period of 12–17 sec, and stable membrane depolarization to between ?40 and ?30 mV, which may lead to the onset of stable rhythmic activity of these neurons. Dependence of the amplitude of the oscillations of potential on the extracellular concentration of Ca, K, and Na ions was calculated and agrees qualitatively with the experimental data of Barker and Gainer [4].     

A model for the characterization of the spatial properties in vestibular neurons

Quantitative study of the static and dynamic response properties of some otolith-sensitive neurons has been difficult in the past partly because their responses to different linear acceleration vectors exhibited no null plane and a dependence of phase on stimulus orientation. The theoretical formulation of the response ellipse provides a quantitative way to estimate the spatio-temporal properties of such neurons. Its semi-major axis gives the direction of the polarization vector (i.e., direction of maximal sensitivity) and it estimates the neuronal response for stimulation along that direction. In addition, the semi-minor axis of the ellipse provides an estimate of the neuron's maximal sensitivity in the null plane. In this paper, extracellular recordings from otolith-sensitive vestibular nuclei neurons in decerebrate rats were used to demonstrate the practical application of the method. The experimentally observed gain and phase dependence on the orientation angle of the acceleration vector in a head-horizontal plane was described and satisfactorily fit by the response ellipse model. In addition, the model satisfactorily fits neuronal responses in three-dimensions and unequivocally demonstrates that the response ellipse formulation is the general approach to describe quantitatively the spatial properties of vestibular neurons.     

Generalized Stein's model for anatomically complex neurons

A neuron with a large dendritic structure is considered. The number of synapses located on the dendrites is substantially higher than on the soma. The synaptic input effect on the neuronal excitability decreases with distance between a synapse ending and the trigger zone. Two areas are distinguished in accordance with the effect of synaptic input--dendritic and somatic. The dendritic area, when compared to the soma, is characterized by much higher intensity of its activation but the amplitudes of synaptically evoked changes of the membrane potential at the trigger zone are in general small. This situation is suitable for a diffusion approximation. However, on the soma, especially in the proximity of the trigger zone, the membrane potential changes are a large fraction of the threshold depolarization. The membrane potential at the trigger zone is modelled by a one-dimensional stochastic process. The diffusion Ornstein-Uhlenbeck process serves as a basis of the model; however, at the moments of somatic synapses activation its voltage changes in jumps. Their sizes represent the amplitudes of the evoked postsynaptic potentials. The unimodal histograms of interspike intervals can be explained by the model. The values of the coefficient of variation greater than one are connected with substantial inhibition.