Using sensory weighting to model the influence of canal,otolith and visual cues on spatial orientation and eye movements

 The sensory weighting model is a general model of sensory integration that consists of three processing layers. First, each sensor provides the central nervous system (CNS) with information regarding a specific physical variable. Due to sensor dynamics, this measure is only reliable for the frequency range over which the sensor is accurate. Therefore, we hypothesize that the CNS improves on the reliability of the individual sensor outside this frequency range by using information from other sensors, a process referred to as “frequency completion.” Frequency completion uses internal models of sensory dynamics. This “improved” sensory signal is designated as the “sensory estimate” of the physical variable. Second, before being combined, information with different physical meanings is first transformed into a common representation; sensory estimates are converted to intermediate estimates. This conversion uses internal models of body dynamics and physical relationships. Third, several sensory systems may provide information about the same physical variable (e.g., semicircular canals and vision both measure self-rotation). Therefore, we hypothesize that the “central estimate” of a physical variable is computed as a weighted sum of all available intermediate estimates of this physical variable, a process referred to as “multicue weighted averaging.” The resulting central estimate is fed back to the first two layers. The sensory weighting model is applied to three-dimensional (3D) visual–vestibular interactions and their associated eye movements and perceptual responses. The model inputs are 3D angular and translational stimuli. The sensory inputs are the 3D sensory signals coming from the semicircular canals, otolith organs, and the visual system. The angular and translational components of visual movement are assumed to be available as separate stimuli measured by the visual system using retinal slip and image deformation. In addition, both tonic (“regular”) and phasic (“irregular”) otolithic afferents are implemented. Whereas neither tonic nor phasic otolithic afferents distinguish gravity from linear acceleration, the model uses tonic afferents to estimate gravity and phasic afferents to estimate linear acceleration. The model outputs are the internal estimates of physical motion variables and 3D slow-phase eye movements. The model also includes a smooth pursuit module. The model matches eye responses and perceptual effects measured during various motion paradigms in darkness (e.g., centered and eccentric yaw rotation about an earth-vertical axis, yaw rotation about an earth-horizontal axis) and with visual cues (e.g., stabilized visual stimulation or optokinetic stimulation). Received: 20 September 2000 / Accepted in revised form: 28 September 2001     

Visual contributions to human self-motion perception during horizontal body rotation

It is still an enigma how human subjects combine visual and vestibular inputs for their self-motion perception. Visual cues have the benefit of high spatial resolution but entail the danger of self motion illusions. We performed psychophysical experiments (verbal estimates as well as pointer indications of perceived self-motion in space) in normal subjects (Ns) and patients with loss of vestibular function (Ps). Subjects were presented with horizontal sinusoidal rotations of an optokinetic pattern (OKP) alone (visual stimulus; 0.025-3.2 Hz; displacement amplitude, 8 degrees) or in combinations with rotations of a Bárány chair (vestibular stimulus; 0.025-0.4 Hz; +/- 8 degrees). We found that specific instructions to the subjects created different perceptual states in which their self-motion perception essentially reflected three processing steps during pure visual stimulation: i) When Ns were primed by a procedure based on induced motion and then they estimated perceived self-rotation upon pure optokinetic stimulation (circular vection, CV), the CV has a gain close to unity up to frequencies of almost 0.8 Hz, followed by a sharp decrease at higher frequencies (i.e., characteristics resembling those of the optokinetic reflex, OKR, and of smooth pursuit, SP). ii) When Ns were instructed to "stare through" the optokinetic pattern, CV was absent at high frequency, but increasingly developed as frequency was decreased below 0.1 Hz. iii) When Ns "looked at" the optokinetic pattern (accurately tracked it with their eyes) CV was usually absent, even at low frequency. CV in Ps showed similar dynamics as in Ns in condition i), independently of the instruction. During vestibular stimulation, self-motion perception in Ns fell from a maximum at 0.4 Hz to zero at 0.025 Hz. When vestibular stimulation was combined with visual stimulation while Ns "stared through" OKP, perception at low frequencies became modulated in magnitude. When Ns "looked" at OKP, this modulation was reduced, apart from the synergistic stimulus combination (OKP stationary) where magnitude was similar as during "staring". The obtained gain and phase curves of the perception were incompatible with linear systems prediction. We therefore describe the present findings by a non-linear dynamic model in which the visual input is processed in three steps: i) It shows dynamics similar to those of OKR and SP; ii) it is shaped to complement the vestibular dynamics and is fused with a vestibular signal by linear summation; and iii) it can be suppressed by a visual-vestibular conflict mechanism when the visual scene is moving in space. Finally, an important element of the model is a velocity threshold of about 1.2 degrees/s which is instrumental in maintaining perceptual stability and in explaining the observed dynamics of perception. We conclude from the experimental and theoretical evidence that self-motion perception normally is related to the visual scene as a reference, while the vestibular input is used to check the kinematic state of the scene; if the scene appears to move, the visual signal becomes suppressed and perception is based on the vestibular cue.     

Multisensory fusion and the stochastic structure of postural sway

 We analyze the stochastic structure of postural sway and demonstrate that this structure imposes important constraints on models of postural control. Linear stochastic models of various orders were fit to the center-of-mass trajectories of subjects during quiet stance in four sensory conditions: (i) light touch and vision, (ii) light touch, (iii) vision, and (iv) neither touch nor vision. For each subject and condition, the model of appropriate order was determined, and this model was characterized by the eigenvalues and coefficients of its autocovariance function. In most cases, postural-sway trajectories were similar to those produced by a third-order model with eigenvalues corresponding to a slow first-order decay plus a faster-decaying damped oscillation. The slow-decay fraction, which we define as the slow-decay autocovariance coefficient divided by the total variance, was usually near 1. We compare the stochastic structure of our data to two linear control-theory models: (i) a proportional–integral–derivative control model in which the postural system's state is assumed to be known, and (ii) an optimal-control model in which the system's state is estimated based on noisy multisensory information using a Kalman filter. Under certain assumptions, both models have eigenvalues consistent with our results. However, the slow-decay fraction predicted by both models is less than we observe. We show that our results are more consistent with a modification of the optimal-control model in which noise is added to the computations performed by the state estimator. This modified model has a slow-decay fraction near 1 in a parameter regime in which sensory information related to the body's velocity is more accurate than sensory information related to position and acceleration. These findings suggest that: (i) computation noise is responsible for much of the variance observed in postural sway, and (ii) the postural control system under the conditions tested resides in the regime of accurate velocity information. Received: 20 March 2001 / Accepted: 17 April 2002 Acknowledgements. We thank Tjeerd Dijkstra for bringing the slow-decay component of postural sway to our attention. Funding for this research was provided by National Institutes of Health grant R29 N35070–01A2, John J. Jeka, PI. Correspondence to: T. Kiemel (Tel.: +1-301-4056176, Fax: +1-301-3149358 e-mail: kiemel@glue.umd.edu)     

Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex

 A kinematical model for excitable wave propagation is analyzed to describe the dynamics of a typical neurological symptom of migraine. The kinematical model equation is solved analytically for a linear dependency between front curvature and velocity. The resulting wave starts from an initial excitation and moves in the medium that represents the primary visual cortex. Due to very weak excitability the wave propagates only across a confined area and eventually disappears. This cortical excitation pattern is projected onto a visual hemifield by reverse retinotopic mapping. Weak excitability explains the confined appearance of aura symptoms in time and sensory space. The affected area in the visual field matches in growth and form the one reported by migraine sufferers. The results can be extended from visual to tactile and to other sensory symptoms. If the spatiotemporal pattern from our model can be matched in future investigations with those from introspectives, it would allow one to draw conclusions on topographic mapping of sensory input in human cortex. Received: 25 April 2002 / Accepted: 20 February 2003 / Published online: 20 May 2003 RID="*" ID="*" Present address: M. A. Dahlem Leibniz-Institut für Neurobiologie, Brenneckestr. 6, 39118 Magdeburg, Germany Acknowledgements. We would like to thank V. Zykov for useful discussions on wave Propagation, and one of us (MAD) would like to thank Ed Chronicle for useful discussions on functional excitability. This project was supported by a scholarship Landesstipendium Sachsen-Anhalt to MAD. Correspondence to: M. A. Dahlem (e-mail: dahlem@ifn-magdeburg.de)     

Wide-field, motion-sensitive neurons and matched filters for optic flow fields

 The receptive field organization of a class of visual interneurons in the fly brain (vertical system, or VS neurons) shows a striking similarity to certain self-motion-induced optic flow fields. The present study compares the measured motion sensitivities of the VS neurons (Krapp et al. 1998) to a matched filter model for optic flow fields generated by rotation or translation. The model minimizes the variance of the filter output caused by noise and distance variability between different scenes. To that end, prior knowledge about distance and self-motion statistics is incorporated in the form of a “world model”. We show that a special case of the matched filter model is able to predict the local motion sensitivities observed in some VS neurons. This suggests that their receptive field organization enables the VS neurons to maintain a consistent output when the same type of self-motion occurs in different situations. Received: 14 June 1999 / Accepted in revised form: 20 March 2000     

A numerical method for renal models that represent tubules with abrupt changes in membrane properties

 The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method. Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002 This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney Diseases, grant DK-42091.) Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45 Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit     

Integration of Semi-Circular Canal and Otolith Cues for Direction Discrimination during Eccentric Rotations

Humans are capable of moving about the world in complex ways. Every time we move, our self-motion must be detected and interpreted by the central nervous system in order to make appropriate sequential movements and informed decisions. The vestibular labyrinth consists of two unique sensory organs the semi-circular canals and the otoliths that are specialized to detect rotation and translation of the head, respectively. While thresholds for pure rotational and translational self-motion are well understood surprisingly little research has investigated the relative role of each organ on thresholds for more complex motion. Eccentric (off-center) rotations during which the participant faces away from the center of rotation stimulate both organs and are thus well suited for investigating integration of rotational and translational sensory information. Ten participants completed a psychophysical direction discrimination task for pure head-centered rotations, translations and eccentric rotations with 5 different radii. Discrimination thresholds for eccentric rotations reduced with increasing radii, indicating that additional tangential accelerations (which increase with radius length) increased sensitivity. Two competing models were used to predict the eccentric thresholds based on the pure rotation and translation thresholds: one assuming that information from the two organs is integrated in an optimal fashion and another assuming that motion discrimination is solved solely by relying on the sensor which is most strongly stimulated. Our findings clearly show that information from the two organs is integrated. However the measured thresholds for 3 of the 5 eccentric rotations are even more sensitive than predictions from the optimal integration model suggesting additional non-vestibular sources of information may be involved.     

A temperature-sensitive DNA adenine methyltransferase mutant of Salmonella typhimurium

A temperature-sensitive mutant of Salmonella typhimurium was isolated earlier after transposon mutagenesis with Tn10d Tet. The mutant D220 grows well at 28 °C but has a lower growth rate and forms filaments at 37 °C. Transposon-flanking fragments of mutant D220 DNA were cloned and sequenced. The transposon was inserted in the dam gene between positions 803 and 804 (assigned allele number: dam-231 : : Tn10d Tet) and resulted in a predicted ten-amino-acid-shorter Dam protein. The insertion created a stop codon that led to a truncated Dam protein with a temperature-sensitive phenotype. The insertion dam-231 : : Tn10d Tet resulted in a dam“leaky” phenotype since methylated and unmethylated adenines in GATC sequences were present. In addition, the dam-231 : : Tn10d Tet insertion rendered dam mutants temperature-sensitive for growth depending upon the genetic background of the S. typhimurium strain. The wild-type dam gene of S. typhimurium exhibited 82% identity with the Escherichia coli dam gene.     

An in silico central pattern generator: silicon oscillator,coupling, entrainment,and physical computation

 In biological systems, the task of computing a gait trajectory is shared between the biomechanical and nervous systems. We take the perspective that both of these seemingly different computations are examples of physical computation. Here we describe the progress that has been made toward building a minimal biped system that illustrates this idea. We embed a significant portion of the computation in physical devices, such as capacitors and transistors, to underline the potential power of emphasizing the understanding of physical computation. We describe results in the exploitation of physical computation by (1) using a passive knee to assist in dynamics computation, (2) using an oscillator to drive a monoped mechanism based on the passive knee, (3) using sensory entrainment to coordinate the mechanics with the neural oscillator, (4) coupling two such systems together mechanically at the hip and computationally via the resulting two oscillators to create a biped mechanism, and (5) demonstrating the resulting gait generation in the biped mechanism. Received: 31 October 2001 / Accepted in revised form: 17 September 2002 Correspondence to: M.A. Lewis     

Mathematical requirements of visual–vestibular integration

This article addresses the intersection between perceptual estimates of head motion based on purely vestibular and purely visual sensation, by considering how nonvisual (e.g. vestibular and proprioceptive) sensory signals for head and eye motion can be combined with visual signals available from a single landmark to generate a complete perception of self-motion. In order to do this, mathematical dimensions of sensory signals and perceptual parameterizations of self-motion are evaluated, and equations for the sensory-to-perceptual transition are derived. With constant velocity translation and vision of a single point, it is shown that visual sensation allows only for the externalization, to the frame of reference given by the landmark, of an inertial self-motion estimate from nonvisual signals. However, it is also shown that, with nonzero translational acceleration, use of simple visual signals provides a biologically plausible strategy for integration of inertial acceleration sensation, to recover translational velocity. A dimension argument proves similar results for horizontal flow of any number of discrete visible points. The results provide insight into the convergence of visual and vestibular sensory signals for self-motion and indicate perceptual algorithms by which primitive visual and vestibular signals may be integrated for self-motion perception.     

Time representing cortical activities: two models inspired by prefrontal persistent activity

 Timing information in the range of seconds is significantly correlated with our behavior. There is growing interest in the cognitive behaviors that rely on perception, comparison, or generation of timing. However, little is known about the neural mechanisms underlying such behaviors. Here we model two different neural mechanisms to represent timing information in the range of seconds. In one model, a recurrent network of bistable spiking neurons shows a quasistable state that is initiated by a brief input and typically lasts for a few to several seconds. The duration of this quasistable activity may be regarded as the neural representation of internal time obeying a psychophysical law of time recognition. Another model uses synfire chains to provide the timing information necessary for predicting the times of anticipated events. In this model, the neurons projected to by multiple synfire chains are conditioned to fire synchronously at the times when an external event (GO signal) is expected. The conditioning is accomplished by spike-timing-dependent plasticity. The two models are inspired by the prefrontal activities of the monkeys engaging in different timing-information-related tasks. Thus, this cortical region may provide the timing information required for organizing various behaviors. Received: 12 March 2002 / Accepted in revised form: 26 November 2002 / Published online: 28 March 2003 Correspondence to: T. Fukai (e-mail: tfukai@eng.tamagawa.ac.jp, Tel.: +81-42-7398434, Fax: +81-42-7397135) Acknowledgements. K. Kitano was supported by Japan Society for the Promotion of Science.     

Cortical network reorganization guided by sensory input features

 Sensory experience alters the functional organization of cortical networks. Previous studies using behavioral training motivated by aversive or rewarding stimuli have demonstrated that cortical plasticity is specific to salient inputs in the sensory environment. Sensory experience associated with electrical activation of the basal forebrain (BasF) generates similar input specific plasticity. By directly engaging plasticity mechanisms and avoiding extensive behavioral training, BasF stimulation makes it possible to efficiently explore how specific sensory features contribute to cortical plasticity. This review summarizes our observations that cortical networks employ a variety of strategies to improve the representation of the sensory environment. Different combinations of receptive-field, temporal, and spectrotemporal plasticity were generated in primary auditory cortex neurons depending on the pitch, modulation rate, and order of sounds paired with BasF stimulation. Simple tones led to map expansion, while modulated tones altered the maximum cortical following rate. Exposure to complex acoustic sequences led to the development of combination-sensitive responses. This remodeling of cortical response characteristics may reflect changes in intrinsic cellular mechanisms, synaptic efficacy, and local neuronal connectivity. The intricate relationship between the pattern of sensory activation and cortical plasticity suggests that network-level rules alter the functional organization of the cortex to generate the most behaviorally useful representation of the sensory environment. Received: 14 January 2002 / Accepted: 15 March 2002 Correspondence to: M.P. Kilgard (e-mail: kilgard@utdallas.edu, Tel.: +1-972-8832345, Fax: +1-972-8832491)     

A rotation and translation invariant discrete saliency network

 We describe a neural network that enhances and completes salient closed contours in images. Our work is different from all previous work in three important ways. First, like the input provided to primary visual cortex (V1) by the lateral geniculate nucleus (LGN), the input to our computation is isotropic. That is, it is composed of spots, not edges. Second, our network computes a well-defined function of the input based on a distribution of closed contours characterized by a random process. Third, even though our computation is implemented in a discrete network, its output is invariant to continuous rotations and translations of the input image. Received: 11 July 2002 / Accepted in revised form: 25 October 2002 Acknowledgements. L.R.W. was supported in part by Los Alamos National Laboratory. J.W.Z. was supported in part by the Albuquerque High Performance Computing Center. We wish to thank Jonas August and Steve Zucker for their insightful comments. Correspondence to: L.R. Williams (e-mail: Williams@cs.unm.edu)     

Fast cortical selection: a principle of neuronal self-organization for perception?

 It is commonly accepted that larger visual objects are represented in the cerebral cortex by specific spatial patterns of neuronal activity. Self-organization is a key concept in the different explanations of such neuronal representations. We here propose as a hypothesis that fast cortical selection (FCS) is an intrinsic functional element of cortical self-organization during perception. Selection is a central concept in theoretical biology which has proved its explanatory power in different fields of our natural and cultural world. The central element in the cortical selection process is the pyramidal cell with its two types of excitatory input. In primary cortical areas one of these inputs comes from any of the sensory organs, determining the topological and typological receptive field properties of the cell and also driving it directly. The other type of input connects reciprocally neighbouring pyramidal cells by axon collaterals and only facilitates the driving input. These two functionally different inputs constitute the elementary selection system working by iterative mutual facilitation as a biological algorithm. A short simulation, based entirely on such biological facts, illustrates the dynamic of this selection process: the activity of cells responding better to the external stimulus ‘grow and survive’ the stimulation, whereas less responsive cells decrease their activity due to competition. Received: 13 June 1995 / Accepted in revised form: 27 May 1997     

Computational model of the cockroach escape behavior: winner and losers in a population code

 I present a comprehensive biologically oriented computational model to account for the escape response of the cockroach on the ground. This model is an expansion of previous work that accounted only for discriminating left from right wind directions [Ezrachi et al. (1999) Biol Cybern 81: 89–99]. The model is composed of computational elements describing the biological processes taking place in the various neurons and includes input which emulates empirical data. With this model it is possible to obtain escape behavior that resembles natural behavior. The model is used to address an ongoing debate as to whether the cockroach's turn direction is determined by computations carried out by the entire neuronal population (PC) or rather by a “winner-take-all” (WTA) mechanism. I suggest that the computation mechanism that underlies the cockroach escape response is composed of both PC and WTA principles. Based on the properties of the suggested new mechanism I denote it a “Darwinian population code.” Received: 26 March 2002 / Accepted in revised form: 24 June 2002 Acknowledgements. I thank H. Parnas for her advice and assistance, J. M. Camhi for helpful comments, and D. Lipson for developing the simulation tools. Correspondence to: E. A. Ezrachi (e-mail: erez@piano.ls.huji.ac.il, Tel.: +972-2-6585818, Fax: +972-2-6585569)     

Exact sampling formulas for multi-type Galton-Watson processes

 Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution. It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions. Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction. Received: 10 June 2001 / Revised version: 21 November 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25 Key words or phrases: Multi-type Galton-Watson process – sampling formula – PCR – mitochondrial DNA     

A maximum neural network approach for N-queens problems

 A novel neural network approach using the maximum neuron model is presented for N-queens problems. The goal of the N-queens problem is to find a set of locations of N queens on an N×N chessboard such that no pair of queens commands each other. The maximum neuron model proposed by Takefuji et al. has been applied to two optimization problems where the optimization of objective functions is requested without constraints. This paper demonstrates the effectiveness of the maximum neuron model for constraint satisfaction problems through the N-queens problem. The performance is verified through simulations in up to 500-queens problems on the sequential mode, the N-parallel mode, and the N ²-parallel mode, where our maximum neural network shows the far better performance than the existing neural networks. Received: 4 June 1996/Accepted in revised form: 13 November 1996     

What can the hippocampal representation of environmental geometry tell us about Hebbian learning?

 The importance of the hippocampus in spatial representation is well established. It is suggested that the rodent hippocampal network should provide an optimal substrate for the study of unsupervised Hebbian learning. We focus on the firing characteristics of hippocampal place cells in morphologically different environments. A hard-wired quantitative geometric model of individual place fields is reviewed and presented as the framework in which to understand the additional effects of synaptic plasticity. Existent models employing Hebbian learning are also reviewed. New information is presented regarding the dynamics of place field plasticity over short and long time scales in experiments using barriers and differently shaped walled environments. It is argued that aspects of the temporal dynamics of stability and plasticity in the hippocampal place cell representation both indicate modifications to, and inform the nature of, the synaptic plasticity in place cell models. Our results identify a potential neural basis for long-term incidental learning of environments and provide strong constraints for the way the unsupervised learning in cell assemblies envisaged by Hebb might occur within the hippocampus. Received: 8 March 2002 / Accepted: 13 June 2002 Acknowledgements. This work was supported by the Medical Research Council of the United Kingdom. Correspondence to: C. Lever or N. Burgess (e-mail: colin.lever@ucl.ac.uk; n.burgess@ucl.ac.uk, Tel.: +44-20-76793388 or 1147, Fax: +44-20-76791306 or 1145)     

Fractal and nonfractal analysis of cell images: comparison and application to neuronal dendritic arborization

 Neurons of the rat spinal cord were stained using the Golgi impregnation method. Successfully impregnated neurons from laminae II, III, and VI were subjected to fractal and nonfractal analyses. Fractal analysis was performed using length-related techniques. Since an application of fractal methods to the analysis of dendrite arbor structures requires caution, we adopted as appropriate a nonfractal method proposing a generalized power-law model with two main nonfractal parameters: (i) the anfractuosity, characterizing the degree of dendritic deviation from straight lines; and (ii) an estimate of the total length of arbor dendrites. The anfractuosity can distinguish between two sets of drawings where the fractal methods failed. We also redefine some basic concepts of fractal geometry, present the ruler-counting method, and propose a new definition of fractal dimension. Received: 5 February 2002 / Accepted: 25 June 2002 Acknowledgement. We thank Ing. Dejan Ristanović for preparing the computer program used in this study. Correspondence to: D. Ristanović (e-mail: dusan@ristanovic.com, Tel.: +381-11-3615767)     

Neuronal network modelling of the effects of anaesthetic agents on somatosensory pathways

 The whole question of consciousness, awareness and depth of anaesthesia is both timely, little understood and deeply challenging. Models of the underlying neural pathway mechanisms/dynamics are necessary for understanding the interactions involved and their structure and function. A neuronal network of the somatosensory pathways is proposed in this paper based on experimental information and physiological investigation into anaesthesia. Existing mathematical neuronal models from the literature have been modified and then employed to describe the dynamics of the proposed pathway network. Effects of anaesthetic agents on the cortex were simulated in the model which describes the evoked cortical responses. By comparison with responses from anaesthetised rats, the model's responses are able to describe the dynamics of typical responses. Thus, the proposed model promises to be valuable for investigating the mechanisms of anaesthesia on the cortex and the effects of brain lesions. Received: 4 March 2002 / Accepted in revised form: 8 July 2002 Correspondence to: D. A. Linkens (e-mail: d.linkens@sheffield.ac.uk, Tel.: +44-114-2225133, Fax: +44-114-2731729) Acknowledgements. C.H. Ting was supported by a postgraduate scholarship from the University of Sheffield.