Efflux of K + from dissociated salamander Müller cells was measured with ion-selective microelectrodes. When the distal end of an isolated cell was exposed to high concentrations of extracellular K + , efflux occurred primarily from the endfoot, a cell process previously shown to contain most of the K + conductance of the cell membrane. Computer simulations of K + dynamics in the retina indicate that shunting ions through the Müller cell endfoot process is more effective in clearing local increases in extracellular K + from the retina than is diffusion through extracellular space. We have suggested that the retinal Müller cell, a specialized astrocyte that spans nearly the entire width of the retina, buffers changes in retinal [K + ] o (4,5). We have shown that amphibian Müller cells are almost exclusively permeable to K + (6) and that 94 percent of the total K + conductance in these cells occurs in the Müller cell endfoot, a process lying adjacent to the vitreous humor (4). This highly asymmetric K + conductance distribution may make the process of K + spatial buffering more powerful than has been recognized. For example, nearly all of the K + current entering Müller cells from regions of increased [K + ] o within the retina may leave the Müller cell endfoot process at the vitreo-retinal border. Thus, the vitreous would function as a large potassium sink.We now present experimental evidence of extracellular K + buffering by Müller cells which utilizes this asymmetric conductance distribution. Dissociated Müller cells from the salamander Ambystoma tigrinum were prepared and maintained as described (4). The distal end of the Müller cell surface was exposed to increased [K + ] o by pressure-ejecting an 85 mM KCl-Ringer solution from an extracellular pipette (approximately 3 µm in tip diameter). Perfusate near this ejection pipette was drawn into a suction pipette (30 µm in diameter) to

Generation of the electroretinogram b-wave is simulated with a computer model representing a dark-adapted amphibian retina. The simulation tests the K+ hypothesis of b-wave generation, which holds that b-wave currents arise from localized Müller cell depolarizations generated by light-evoked increases in extracellular K+ concentration, [K+]o. The model incorporates the following components and processes quantitatively: 1) two time-dependent K+ sources representing the light-evoked [K+]o increases in the inner and outer plexiform layers, 2) a time- and [K+]o-dependent K+ sink representing the [K+]o decrease in the rod inner segment layer, 3) diffusion of released K+ through extracellular space, 4) active K+ reuptake and passive K+ drift across the Müller cell membrane, 5) spatial variations in the tortuosity factor and the volume fraction of extracellular space, 6) an extraretinal shunt resistance. Müller cells are modeled with 1) cytoplasmic resistance, 2) spatial variations in membrane permeability to K+, and 3) a membrane potential specified by the Nernst equation and transmembrane current flow. For specified K+ source and sink densities, the model computes [K+]o variations in time and retinal depth. Based on these [K+]o distributions, Müller cell potentials, current source-density profiles, and intraretinal and transretinal voltages are calculated. Imposed [K+]o distributions similar to those seen experimentally during the b-wave lead to the generation of a transient b-wave response and to a prolonged Müller response in the model system. These response time courses arise because the b-wave is dominated by the short-lived distal [K+]o increase, while the Müller response primarily reflects the long-lived proximal [K+]o increase. Current source-density distributions and intraretinal voltage profiles that are generated by the model at the peak of the b-wave closely resemble experimental results. The model generates a realistic slow PIII potential in response to prolonged [K+]o decreases in the distal retina and reproduces the K+ ejection results of Yanagida and Tomita (50) accurately. Simulations also suggest that tissue damage caused by K+-selective micropipettes in experimental preparations can lead to an underestimation of the distal [K+]o increase. The simulations demonstrate that the spatiotemporal properties of intraretinal b-wave voltages and currents and Müller cell responses can be generated according to the K+ hypothesis: by passive Müller cell depolarization driven by variations in [K+]o.

A one-dimensional numerical model of potassium dynamics in the central nervous system is developed. The model incorporates the following physiological processes in computing spatial and temporal changes in extracellular K+ concentration, [K+],: 1) the release of K + from K+ sources into extracellular space, 2) diffusion of Kf through extracellular space, 3) active uptake of K + into cells and blood vessels, 4) passive uptake of K+ into a cellular distribution space, and 5) the transfer of K + by K + spatial buffer current flow in glial cells. The following tissue parameters can be specified along the single spatial dimension of the model: 1) the volume fraction and tortuosity of extracellular and glial cell spaces, 2) the volume fraction of the cellular distribution space, 3) rate constants of active uptake and passive uptake processes, and 4) glial cell membrane conductance. The model computes variations in [K+], and current flow through glial cells for three tissue geometries: 1) planar geometry (the retina and the surface of the brain), 2) cylindrical geometry (tissue surrounding a blood vessel), and 3) spherical geometry (tissue surrounding a point source of Kf). For simple sources of K f , the performance of the model matches that predicted from analytical equations. Simulations of previous ion dynamics experiments indicate that the model can accurately predict ion diffusion and K+ current flow in the brain. Simulations of electroretinogram generation and K + siphoning onto blood vessels suggest that unanticipated K' dynamics mechanisms may be operating in the central nervous system.

This work describes a modelling method for a non-linear system which is based on a multi-point linear approximation for a model predictive control (MPC) purpose. The method is derived from artificial neural network techniques and exploits good properties of a Orthogonal Activation Function based Neural Network (OAF-NN). In this work, we describe a technique of a Explicit-MPC (EMPC) which performance, ease of implementation and extension for the hybrid system gives promising direction of a algorithm design for the embedded systems (ES). Proposed modelling procedure is characterized by fast training property and wide applicability in medical systems, automotive, power-electronics industry etc.. Linearity of the model allows to transform into Piecewise Affine (PWA) system structure and to exploit existing algorithms for a explicit model predictive control design. The applicability of the technique was evaluated on a hybrid system by means of existing software tools for MPC design.