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People with degenerative retinal diseases such as retinitis pigmentosa lose most of their photoreceptors but retain a significant proportion (~30%) of their retinal ganglion cells (RGCs). Microelectronic retinal prostheses aim to bypass the lost photoreceptors and restore vision by directly stimulating the surviving RGCs. Here we investigate the extent to which electrical stimulation of RGCs can evoke neural spike trains with statistics resembling those of normal visually-evoked responses. Whole-cell patch clamp recordings were made from individual cat RGCs in vitro. We first recorded the responses of each cell to short sequences of visual stimulation. These responses were converted to trains of electrical stimulation that we then presented to the same cell via an epiretinal stimulating electrode. We then quantified the efficacy of the electrical stimuli and the latency of the evoked spikes. In all cases, spikes were evoked with sub-millisecond latency (0.55 ms, median, ON cells, n = 8; 0.75 ms, median, OFF cells, n = 6) and efficacy ranged from 0.4-1.0 (0.79, median, ON cells; 0.97, median, OFF cells). These data demonstrate that meaningful spike trains, resembling normal responses of RGCs to visual stimulation, can be reliably evoked by epiretinal prostheses.

Neurons in the primary visual cortex are often classified as either simple or complex based on the linearity (or otherwise) of their response to spatial luminance contrast. In practice, classification is typically based on Fourier analysis of a cell's response to an optimal drifting sine-wave grating. Simple cells are generally considered to be linear and produce responses modulated at the fundamental frequency of the stimulus grating. In contrast, complex cells exhibit significant nonlinearities that reduce the response at the fundamental frequency. Cells can therefore be easily and objectively classified based on the relative modulation of their responses - the ratio of the phase-sensitive response at the fundamental frequency of the stimulus (F₁) to the phase-invariant sustained response (F₀). Cells are classified as simple if F₁/F₀>1 and complex if F₁/F₀<1. This classification is broadly consistent with criteria based on the spatial organisation of cells' receptive fields and is accordingly presumed to reflect disparate functional roles of simple and complex cells in coding visual information. However, Fourier analysis of spiking responses is sensitive to the number of spikes available - F₁/F₀ increases as the number of spikes is reduced, even for phase-invariant complex cells. Moreover, many complex cells encountered in the laboratory exhibit some phase sensitivity, evident as modulation of their responses at the fundamental frequency. There currently exists no objective quantitative means of assessing the significance or otherwise of these modulations. Here we derive a statistical basis for objectively assessing whether the modulation of neuronal responses is reliable, thereby adding a level of statistical certainty to measures of phase sensitivity. We apply our statistical analysis to neuronal responses to moving sine-wave gratings recorded from 367 cells in cat primary visual cortex. We find that approximately 60% of complex cells exhibit statistically significant (α<0.01) modulation of their responses to optimal moving gratings. These complex cells are phase sensitive and reliably encode spatial phase., (Copyright © 2013 IBRO. Published by Elsevier Ltd. All rights reserved.)

There are 16 morphologically defined classes of rats retinal ganglion cells (RGCs). Using computer simulation of a realistic anatomically correct A1 mouse RGC, we investigate the effect of the cell's morphology on its impulse waveform, using the first-, and second-order time derivatives as well as the phase plot features. Using whole cell patch clamp recordings, we recorded the impulse waveform for each of the rat RGCs types. While we found some clear differences in many features of the impulse waveforms for A2 and B2 cells compared to other cell classes, many cell types did not show clear differences.

Mammalian retina contains 15-20 different retinal ganglion cell (RGC) types, each of which is responsible for encoding different aspects of the visual scene. The encoding is defined by a combination of RGC synaptic inputs, the neurotransmitter systems used, and their intrinsic physiological properties. Each cell's intrinsic properties are defined by its morphology and membrane characteristics, including the complement and localization of the ion channels expressed. In this study, we examined the hypothesis that the intrinsic properties of individual RGC types are conserved among mammalian species. To do so, we measured the intrinsic properties of 16 morphologically defined rat RGC types and compared these data with cat RGC types. Our data demonstrate that in the rat different morphologically defined RGC types have distinct patterns of intrinsic properties. Variation in these properties across cell types was comparable to that found for cat RGC types. When presumed morphological homologs in rat and cat retina were compared directly, some RGC types had very similar properties. The rat A2 cell exhibited patterns of intrinsic properties nearly identical to the cat alpha cell. In contrast, rat D2 cells (ON-OFF directionally selective) had a very different pattern of intrinsic properties than the cat iota cell. Our data suggest that the intrinsic properties of RGCs with similar morphology and suspected visual function may be subject to variation due to the behavioral needs of the species.

In this paper we aim to quantify the effect of the inner limiting membrane (ILM) of the retina on the thresholds for epiretinal electrical stimulation of retinal ganglion cells by a microelectronic retinal prosthesis. A pair of bipolar stimulating electrodes was placed either above (on the epiretinal surface) or below the ILM while we made whole-cell patch-clamp recordings from retinal ganglion cells in an isolated rat retinal whole-mount preparation. Across our cell population we found no significant difference in the median threshold stimulus amplitudes when the stimulating electrodes were placed below as opposed to above the ILM (p = 0.08). However, threshold stimulus amplitudes did tend to be lower when the stimulating electrodes were placed below the ILM (30 µA vs 56 µA).

In surveying their visual environment, primates, including humans make frequent rapid eye movements known as saccades. Saccades result in rapid motion of the retinal image and yet this motion is not perceived. We recorded saccade-related changes in neural activity in the dorsal medial superior temporal area (MSTd) of alert macaque monkeys. We show that the spontaneous activity of neurons in MSTd is modulated around the time of saccades. Some cells show considerable suppression of spontaneous activity, while most show early and significant enhancement. While this modulation of spontaneous activity is variable, the concomitant modulation of neural responses evoked by flashed visual stimuli is uniform and stereotypical - visual responses are suppressed for stimuli presented around the time of saccades and enhanced for stimuli presented afterwards. The combined modulation of spontaneous activity and evoked visual responses likely serves to reduce the detectability of peri-saccadic stimuli and promote the perceptual awareness of visual stimuli between saccades., (Copyright © 2010 Elsevier Ltd. All rights reserved.)

Simple cells in the primary visual cortex have segregated ON and OFF subregions in their receptive fields, while complex cells have overlapping ON and OFF subregions. These two cell types form the extremes at each end of a continuum of receptive field types. Hubel and Wiesel in 1962 suggested a hierarchical scheme of processing whereby spatially offset simple cells drive complex cells. Simple and complex cells are often classified by their responses to moving sine wave gratings: simple cells have oscillatory responses while complex cells produce unmodulated responses. Here, using moving gratings as stimuli, we show that a significant number of cells that display low levels of response modulation at high contrasts demonstrate high levels of response modulation at low contrasts. Most often a drifting low contrast grating generates a large phasic response at the fundamental frequency of the grating (F(1)) and a smaller but significant phasic response that is approximately 180 deg out-of-phase with the F(1) component. We present several models capable of capturing the effects of stimulus contrast on complex cell responses. The model that best reproduces our experimental results is a variation of the classical hierarchical model. In our model several spatially offset simple cells provide input to a complex cell, with each simple cell exhibiting a different contrast response function. At low contrasts only one of these simple cells is sufficiently excited to reveal its receptive field properties. As contrast is increased additional spatially offset simple cells with higher contrast thresholds add their responses to the overall spiking activity.

A lumped parameter model of human cardiovascular-implantable rotary blood pump (iRBP) interaction has been developed based on experimental data recorded in two healthy pigs with the iRBP in situ. The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, as well as the iRBP. A subset of parameters was optimized in a least squares sense to faithfully reproduce the experimental measurements (pressures, flows and pump variables). Our fitted model compares favorably with our experimental measurements at a range of pump operating points. Furthermore, we have also suggested the importance of various model features, such as the curvilinearity of the end systolic pressure-volume relationship, the Starling resistance, the suction resistance, the effect of respiration, as well as the influence of the pump inflow and outflow cannulae. Alterations of model parameters were done to investigate the circulatory response to rotary blood pump assistance under heart failure conditions. The present model provides a valuable tool for experiment designs, as well as a platform to aid in the development and evaluation of robust physiological pump control algorithms.

Perceived contrast is reduced after prolonged exposure to a textured pattern (contrast adaptation). The size of this effect is dependent on the relationship between the adapting contrast and the test contrast. It is generally accepted that the greatest reductions occur when the adapting contrast is much higher than the test contrast. Here this relationship was examined for a wide range of spatial frequencies. The results show that the effect of the adapt/test ratio on perceived contrast following contrast adaptation is highly spatial frequency dependent. At high spatial frequencies >1cpd perceived contrast was reduced for all adapting contrasts, which is consistent with other studies. However, at low spatial frequencies (<1cpd) the perceived contrast was actually above veridical perception when the adapting contrast was lower than the test contrast. This finding has not been previously reported and has important implications for models of contrast perception.

We performed optical intrinsic signal imaging of cat primary visual cortex (Area 17 and 18) while delivering bipolar electrical stimulation to the retina by way of a supra-choroidal electrode array. Using a general linear model (GLM) analysis we identified statistically significant (p < 0.01) activation in a localized region of cortex following supra-threshold electrical stimulation at a single retinal locus., Our Results: (1) demonstrate that intrinsic signal imaging combined with linear model analysis provides a powerful tool for assessing cortical responses to prosthetic stimulation, and (2) confirm that supra-choroidal electrical stimulation can achieve localized activation of the cortex consistent with focal activation of the retina.

Although we don't perceive visual stimuli during saccadic eye movements, new evidence shows that our brains do process these stimuli and they can influence our subsequent visual perception.

Humans use saccadic eye movements to make frequent gaze changes, yet the associated full-field image motion is not perceived. The theory of saccadic suppression has been proposed to account for this phenomenon, but it is not clear whether suppression originates from a retinal signal at saccade onset or from the brain before saccade onset. Perceptually, visual sensitivity is reduced before saccades and enhanced afterward. Over the same time period, the perception of time is compressed and even inverted. We explore the origins and neural basis of these effects by recording from neurons in the dorsal medial superior temporal area (MSTd) of alert macaque monkeys. Neuronal responses to flashed presentations of a textured pattern presented at random times relative to saccades exhibit a stereotypical pattern of modulation. Response amplitudes are strongly suppressed for flashes presented up to 90 ms before saccades. Immediately after the suppression, there is a period of 200-450 ms in which flashes generate enhanced response amplitudes. Our results show that (1) MSTd is not directly suppressed, rather suppression is inherited from earlier visual areas; (2) early suppression of the visual system must be of extra-retinal origin; (3) postsaccadic enhancement of neural activity occurs in MSTd; and (4) the enhanced responses have reduced latencies. As a whole, these observations reveal response properties that could account for perceptual observations relating to presaccadic suppression, postsaccadic enhancement and time compression.

Accurate noninvasive average flow and differential pressure estimation of implantable rotary blood pumps (IRBPs) is an important practical element for their physiological control. While most attempts at developing flow and differential pressure estimate models have involved purely empirical techniques, dimensional analysis utilizes theoretical principles of fluid mechanics that provides valuable insights into parameter relationships. Based on data obtained from a steady flow mock loop under a wide range of pump operating points and fluid viscosities, flow and differential pressure estimate models were thus obtained using dimensional analysis. The algorithm was then validated using data from two other VentrAssist IRBPs. Linear correlations between estimated and measured pump flow over a flow range of 0.5 to 8.0 L/min resulted in a slope of 0.98 ( R(2) = 0.9848). The average flow error was 0.20 +/- 0.14 L/min (mean +/- standard deviation) and the average percentage error was 5.79%. Similarly, linear correlations between estimated and measured pump differential pressure resulted in a slope of 1.027 ( R(2) = 0.997) over a pressure range of 60 to 180 mmHg. The average differential pressure error was 1.84 +/- 1.54 mmHg and the average percentage error was 1.51%.

By way of extracellular, stimulating electrodes, a microelectronic retinal prosthesis aims to render discrete, luminous spots-so-called phosphenes-in the visual field, thereby providing a phosphene image (PI) as a rudimentary remediation of profound blindness. As part thereof, a digital camera, or some other photosensitive array, captures frames, frames are analyzed, and phosphenes are actuated accordingly by way of modulated charge injections. Here, we present a method that allows the assessment of image analysis schemes for integration with a prosthetic device, that is, the means of converting the captured image (high resolution) to modulated charge injections (low resolution). We use the mutual-information function to quantify the amount of information conveyed to the PI observer (device implantee), while accounting for the statistics of visual stimuli. We demonstrate an effective scheme involving overlapping, Gaussian kernels, and discuss extensions of the method to account for shortterm visual memory in observers, and their perceptual errors of omission and commission.

An integral component in the development of a control strategy for implantable rotary blood pumps is the task of reliably detecting the occurrence of left ventricular collapse due to overpumping of the native heart. Using the noninvasive pump feedback signal of impeller speed, an approach to distinguish between overpumping (or ventricular collapse) and the normal pumping state has been developed. Noninvasive pump signals from 10 human pump recipients were collected, and the pumping state was categorized as either normal or suction, based on expert opinion aided by transesophageal echocardiographic images. A number of indices derived from the pump speed waveform were incorporated into a classification and regression tree model, which acted as the pumping state classifier. When validating the model on 12,990 segments of unseen data, this methodology yielded a peak sensitivity/specificity for detecting suction of 99.11%/98.76%. After performing a 10-fold cross-validation on all of the available data, a minimum estimated error of 0.53% was achieved. The results presented suggest that techniques for pumping state detection, previously investigated in preliminary in vivo studies, are applicable and sufficient for use in the clinical environment.

Methods of speed control for implantable rotary blood pumps (iRBPs) are vital for providing implant recipients with sufficient blood flow to cater for their physiological requirements. The detection of pumping states that reflect the physiological state of the native heart forms a major component of such a control method. Employing data from a number of acute animal experiments, five such pumping states have been previously identified: regurgitant pump flow, ventricular ejection (VE), nonopening of the aortic valve (ANO), and partial collapse (intermittent [PVC-I] and continuous [PVC-C]) of the ventricle wall. An automated approach that noninvasively detects such pumping states, employing a classification and regression tree (CART), has also been developed. An extension to this technique, involving an investigation into the effects of cardiac rhythm disturbances on the state detection process, is discussed. When incorporating animal data containing arrhythmic events into the CART model, the strategy showed a marked improvement in detecting pumping states as compared to the model devoid of arrhythmic data: state VE--57.4/91.7% (sensitivity/specificity) improved to 97.1/100.0%; state PVC-I--66.7/83.1% improved to 100.0/88.3%, and state PVC-C--11.1/66.2% changed to 0.0/100%. With a simplified binary scheme differentiating suction (PVC-I, PVC-C) and nonsuction (VE, ANO) states, suction was initially detected with 100/98.5% sensitivity/specificity, whereas with the subsequent improved model, both these states were detected with 100% sensitivity. The accuracy achieved demonstrates the robustness of the technique presented, and substantiates its inclusion into any iRBP control methodology.

The effect of blood hematocrit (HCT) on a noninvasive flow estimation algorithm was examined in a centrifugal implantable rotary blood pump (iRBP) used for ventricular assistance. An average flow estimator, based on three parameters, input electrical power, pump speed, and HCT, was developed. Data were collected in a mock loop under steady flow conditions for a variety of pump operating points and for various HCT levels. Analysis was performed using three-dimensional polynomial surfaces to fit the collected data for each different HCT level. The polynomial coefficients of the surfaces were then analyzed as a function of HCT. Linear correlations between estimated and measured pump flow over a flow range from 1.0 to 7.5 L/min resulted in a slope of 1.024 L/min (R2=0.9805). Early patient data tested against the estimator have shown promising consistency, suggesting that consideration of HCT can improve the accuracy of existing flow estimation algorithms.

We have developed a finite-element surface model of human atria, in order to study normal and abnormal patterns of atrial activation. To characterize electrical activity in both atrial muscle and cardiac pacemaker regions, Fitzhugh-Nagumo-type equations were employed. Model equations were tested using a simplified geometry containing major topological features of both atria. The model is able to generate spontaneous activation of electrical impulses within the sinoatrial node which propagate across the atria. The model can be used as a basis for investigating mechanisms underlying normal and abnormal atrial rhythms, including re-entrant activation by an ectopic focus.

A noninvasive approach to the task of pulsatile flow estimation in an implantable rotary blood pump (iRBP) has been proposed. Employing six fluid solutions representing a range of viscosities equivalent to 20-50% blood hematocrit (HCT), pulsatile flow data was acquired from an in vitro mock circulatory loop. The entire operating range of the pump was examined, including flows from -2 to 12 L/min. Taking the pump feedback signals of speed and power, together with the HCT level, as input parameters, several flow estimate models were developed via system identification methods. Three autoregressive with exogenous input (ARX) model structures were evaluated: structures I and II used the input parameters directly; structure II incorporated additional terms for HCT; and the third structure employed as input a non-pulsatile flow estimate equation. Optimal model orders were determined, and the associated models yielded minimum mean flow errors of 5.49% and 0.258 L/min for structure II, and 5.77% and 0.270 L/min for structure III, when validated on unseen data. The models developed in this study present a practical method of accurately estimating iRBP flow in a pulsatile environment.

A lumped parameter model of the cardiovascular system (CVS) and its interaction with an implantable rotary blood pump (iRBP) is presented. The CVS model consists of the heart, the systemic and the pulmonary circulations. The pump model is made up of three differential equations, i.e. the motor equation, the torque equation and the hydraulic equation. Qualitative comparison with data from ex vivo porcine experiments suggests that the model is able to simulate different physiologically significant pumping states with varying pump speed set points. The combined CVS-iRBP model is suitable for use as a tool for investigating changes in the circulatory system parameters in the presence of the pump, and for testing control algorithms.

Microelectronic retinal prostheses have been shown to restore the perception of light to the blind through electrical stimulation. Conventional recording techniques such as recording electrode arrays on the visual cortex can give a basic understanding of the events that occur during such stimulation events, but their finite size and number limits the spatial resolution achievable with them. Optical imaging of intrinsic signals (OIS imaging) allows for greater resolution (approximately 50 microm) of the activity in the cortex. This can be used to facilitate a greater understanding of the complex neurophysiological events that allow prosthetic vision. This paper shows responses to visual and electrical stimulation of the retina, and demonstrates that OIS imaging may be an effective technique in further refining stimulation techniques and implant designs for retinal prostheses.

Optical imaging of intrinsic signals (OIS) is a tool for visualizing differential areas in the primary visual cortex devoted to visual functions such as ocular dominance and spatial orientation preferences. The OIS methodology was employed to verify visual cortical response to a retinal vision prosthesis whereby electrical stimulation is applied to the neural retina in order to elicit visual percepts. However, OIS recording is quite susceptible to cardiac and respiratory artifact, and inherent noise related to the measurement process. This complicates the identification of evoked signals using standard ensemble averaging based image processing. We therefore developed an independent component analysis (ICA) "harmonic filtering" technique to improve the signal-to-noise ratio. This technique is capable of reducing noise components, highlighting response signals to visual and electrical stimuli. Particularly, we demonstrated extraction of an ocular dominance map due to corneal stimulation and localized cortical activation due to intravitreal stimulation.

In a clinical setting it is necessary to control the speed of rotary blood pumps used as left ventricular assist devices to prevent possible severe complications associated with over- or underpumping. The hypothesis is that by using only the noninvasive measure of instantaneous pump impeller speed to assess flow dynamics, it is possible to detect physiologically significant pumping states (without the need for additional implantable sensors). By varying pump speed in an animal model, five such states were identified: regurgitant pump flow, ventricular ejection (VE), nonopening of the aortic valve over the cardiac cycle (ANO), and partial collapse (intermittent and continuous) of the ventricle wall (PVC-I and PVC-C). These states are described in detail and a strategy for their noninvasive detection has been developed and validated using (n = 6) ex vivo porcine experiments. Employing a classification and regression tree, the strategy was able to detect pumping states with a high degree of sensitivity and specificity: state VE-99.2/100.0% (sensitivity/specificity); state ANO-100.0/100.0%; state PVC-I- 95.7/91.2%; state PVC-C-69.7/98.7%. With a simplified binary scheme differentiating suction (PVC-I, PVC-C) and nonsuction (VE, ANO) states, both such states were detected with 100% sensitivity.

In this paper, we investigate the role of sinoatrial node (SAN) cellular heterogeneity in two key aspects of normal cardiac pacemaker function: frequency entrainment of the SAN, and propagation of excitation into the atrial tissue. Using detailed ionic models of electrical activity in SAN and atrial myocytes, we have formulated a number of one-dimensional models of SAN heterogeneity based on discrete-region (in which central and peripheral SAN type cell are separated into discrete regions), gradient and mosaic models of SAN organization. Each of the different models were assessed on their ability to achieve frequency entrainment of the SAN and activation of the adjoining atrial tissue in the presence of both uniform and linearly increasing conductivity profiles. Simulation results suggest that the gradient model of SAN heterogeneity, in which cells display a smooth variation in membrane properties from the center to the periphery of the SAN, produces action potential waveshapes and a site of earliest activation consistent with experimental observations in the intact SAN. The gradient model also achieves frequency entrainment of the SAN more easily than other models of SAN heterogeneity. Based on these results, we conclude that the gradient model of SAN heterogeneity, in the presence of a uniform conductivity profile, is the most likely model of SAN organization.

For pt.I see ibid., p.Z004024-7. For pt.II see ibid., p.Z004558-61. This paper examines the rendering of luminous spots ("phosphenes") in the visual field, and their stochastic positioning as a means of anti-aliasing the resulting spotty image ("phosphene image"). We derive an equation concerning the correlations of pairs of phosphenes comprising the phosphene image, and show the relationship to the statistics governing the stochastic positioning. We present some examples where stochastic rendering assists the veridical perception of textures, and argue for its superiority as cf. ordered rendering. Our preliminary results suggest that it may be perceptually effective to manufacture disordered arrays of stimulating electrodes for intraocular implantation.

With respect to rotary blood pumps used as left ventricular assist devices (LVADs), it is clinically important to control pump flow to avoid complications associated with over-or under-pumping of the native heart. By employing only the non-invasive observer of instantaneous pump impeller speed to assess flow dynamics, a number of physiologically significant pumping states may be detected. Based on a number of acute animal experiments, five such states were identified: regurgitant pump flow (PR), ventricular ejection (VE), non-opening of the aortic valve (ANO), and partial collapse (intermittent and continuous) of the ventricle wall (PVC-I and PVC-C). Two broader states, normal (corresponding to VE, ANO) and suction (corresponding to PVC-I, PVC-C) were readily discernable in clinical data from human patients implanted with LVADs. Based on data from both the animal experiments (N=6) and the human patients (N=10), a strategy for the automated non-invasive detection of significant pumping states has been developed and validated. Employing a classification and regression tree (CART), this system detects pumping states with a high degree of accuracy: state VE -87.5/100.0% (sensitivity/specificity); state ANO - 98.1/92.5%; state PVC-I - 90.0/90.2%; state PVC-C - 61.2/98.0%. With a simplified binary scheme differentiating suction and normal states, both states were detected without error in data from the animal experiments, and with a sensitivity/specificity, for detecting suction, of 99.2/98.3% in the human patient data.

Stimulation of the diseased retina via an intraocular electrode array is a proposed means of restoring some vision to the profoundly blind. A prosthetic device to this end would involve post-implantation calibration (analogous to cochlear implant fitting), wherein the subject indicates those discrete positions in the visual field where luminous percepts are elicited. This procedure would be a source of noise, because the indicated positions would only approximate the actual positions in the visual field. Put differently, the procedure introduces sampling jitter, and would therefore affect clinical outcomes such as mobility and reading speeds. The nature of this noise is the concern of the present paper; we derive an expression for the noise power spectrum as it relates to the statistical nature of the sampling jitter. We show that, generally, jitter has greater effect on higher spatial-frequencies, that is, those areas of the implantee's visual perception that represent fine detail are more prone to noise. More specifically, the noise spectrum depends on the characteristic function of the random variable describing the sampling jitter. Our results signal the need for experimental work that characterizes sampling jitter in implantees, plus the need for simulations that allow a better understanding of perception and the noisy phosphene image.

A simplified mathematical model has been developed in order to better understand local current spread when multiple simultaneous current sources are used in an epiretinal neuroprosthesis. To test the model, pairs of platinum electrodes of 430 &#956;m diameter and an intra-pair spacing of 1 mm between centers, were arranged either in-line or in parallel, in a bath of physiological saline. Each pair was separated by distances from 1 mm to 6 mm. The currents in each electrode in the bath were measured and compared with the computational model of the same arrangement. This approach allowed us to quantify return current interaction between parallel sources. As predicted, with parallel electrodes and matching currents in each electrode pair, there is no current cross-talk. However with imbalanced current sources, significant cross-talk is evident. The cross-talk decreases as a function of electrode pair separation. The implication of this work in the design of an epiretinal neuroprosthesis is discussed.

We have formulated a spatial-gradient model of action potential heterogeneity within the rabbit sinoatrial node (SAN), based on cell-specific ionic models of electrical activity from its central and peripheral regions. The ionic models are derived from a generic cell model, incorporating five background and exchange currents, and seven time-dependent currents based on three- or four-state Markov schemes. State transition rates are given by non-linear sigmoid functions of membrane potential. By appropriate selection of parameters, the generic model is able to accurately reproduce a wide range of action potential waveforms observed experimentally. Specifically, the model can fit recordings from central and peripheral regions of the SAN with RMS errors of 0.3987 and 0.7628 m V, respectively. Using a custom least squares parameter optimisation routine, we have constructed a spatially-varying gradient model that exhibits a smooth transition in action potential characteristics from the central to the peripheral region, whilst ensuring individual membrane currents remain physiologically accurate. Smooth transition action potential characteristics include maximum diastolic potential, overshoot potential, upstroke velocity, action potential duration and cycle length. The gradient model is suitable for developing higher dimensional models of the right atrium, in which action potential heterogeneity within nodal tissue may be readily incorporated., (Copyright 2004 Elsevier Ltd.)

The holy grail of biomedical modelling is an integrated model of the entire human body. To this end, research groups around the world need to interchange experimental data, models and model results. A good interchange will have an efficient representation for storage and sharing and will have tools for modelling, data verification, authoring, data conversions and so on. A field is a spatially varying properly. In this paper we present the abstract field layer (AFL) and the field representation language (FRL). The AFL provides the field abstraction together with a set of common field operations. The FRL provides an efficient means for field representation and storage. We show how fields can be used to interchange information between modelling systems and between modelling and visualisation systems. We are currently developing a software system that composes multiple single cell solvers to create a tissue solver.

In this paper, we have employed ionic models of sinoatrial node cells to investigate the synchronization of a pair of coupled cardiac pacemaker cells from central and peripheral regions of the sinoatrial node. The free-running cycle length of the cell models was perturbed using two independent techniques and the minimum coupling conductance required to achieve frequency entrainment was used to assess the relative ease with which various cell pairs achieve entrainment. The factors effecting entrainment were further investigated using single-cell models paced with an artificial biphasic coupling current. Our simulation results suggest that dissimilar cell types, those with largely different upstroke velocities entrain more easily, that is, they require less coupling conductance to achieve 1:1 frequency entrainment. We, therefore, propose that regional variation in action-potential waveshape within the sinoatrial node assists frequency synchronization in vivo.

Paradoxical stable entrainment of heart rate to inhibitory vagal impulses can be simulated with two distinct mathematical models; a complex ionic current model of sinoatrial node pacemaker activity, as well as a simple integrator with non-linear feedback. We show that both models exhibit similar entrainment characteristics to repetitive vagal stimuli. By applying a sharp disturbance to each model whilst entrained, the subsequent path of cycle length recovery can be described by dynamic phase response curves and phase-phase plots, the properties of which dictate whether stable entrainment is possible.