Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Analysis of multiple shared channel cooperative routing in OFDM based wireless networks

Diversity techniques have long been used to combat the channel fading in wireless communications systems. Recently cooperative communications has attracted lot of attention due to many benefits it offers. Thus cooperative routing protocols with diversity transmission can be developed to exploit the random nature of the wireless channels to improve the network efficiency by selecting multiple cooperative nodes to forward data. In this paper we analyze and evaluate the performance of a novel routing protocol with multiple cooperative nodes which share multiple channels. Multiple shared channels cooperative (MSCC) routing protocol achieves diversity advantage by using cooperative transmission. It unites clustering hierarchy with a bandwidth reuse scheme to mitigate the co-channel interference. Theoretical analysis of average packet reception rate and network throughput of the MSCC protocol are presented and compared with simulated results.

Ergodic capacity of the exponentially correlated slotted amplify and forward relay channel

In this paper we analyze the performance degradation of slotted amplify-and-forward protocol in wireless environments with high node density where the number of relays grows asymptotically large. Channel gains between source-destination pairs in such networks can no longer be independent. We analyze the degradation of performance in such wireless environments where channel gains are exponentially correlated by looking at the capacity per channel use. Theoretical results for eigenvalue distribution and the capacity are derived and compared with the simulation results. Both analytical and simulated results show that the capacity given by the asymptotic mutual information decreases with the network density.

Analysis of rural MUSA-MIMO-OFDM uplink channel capacity

Multi-user single antenna multiple-input multiple-output orthogonal frequency division multiplexing (MUSA-MIMO-OFDM) is a promising technology to improve the spectrum efficiency of fixed wireless broadband access systems in rural areas. This letter investigates the capacity of MUSA-MIMO-OFDM uplink channel by theoretical, simulation, and empirical approaches considering up to six users. We propose an empirical capacity formula suitable for rural areas. Characteristics of channel capacity temporal variations and their relationship with the wind speed, observed in a rural area, are also presented in this letter.

Prediction and measurement of multiuser MIMO-OFDM channel in rural Australia

Commonwealth Scientific and Industrial Research Organization (CSIRO) has recently conducted a technology demonstration of a novel fixed wireless broadband access system in rural Australia. The system is based on multi user multiple-input multiple-output orthogonal frequency division multiplexing (MU-MIMO-OFDM). It demonstrated an uplink of six simultaneous users with distances ranging from 10 m to 8.5 km from a central tower, achieving 20 bits s/Hz spectrum efficiency. This paper reports on the analysis of channel capacity and bit error probability simulation based on the measured MUMIMO-OFDM channels obtained during the demonstration, and their comparison with the results based on channels simulated by a novel geometric optics based channel model suitable for MU-MIMO OFDM in rural areas. Despite its simplicity, the model was found to predict channel capacity and bit error rate probability accurately for a typical MU-MIMO-OFDM deployment scenario.

Time-varying bispectral analysis of auditory evoked multi-channel scalp EEG

Time-varying bispectra, computed using a classical sliding window short-time Fourier approach, are analyzed for scalp EEG potentials evoked by an auditory stimulus and new observations are presented. A single, short duration tone is presented from the left or the right, direction unknown to the test subject. The subject responds by moving the eyes to the direction of the sound. EEG epochs sampled at 200 Hz for repeated trials are processed between -70 ms and +1200 ms with reference to the stimulus. It is observed that for an ensemble of correctly recognized cases, the best matching timevarying bispectra at (8 Hz, 8Hz) are for PZ-FZ channels and this is also largely the case for grand averages but not for power spectra at 8 Hz. Out of 11 subjects, the only exception for time-varying bispectral match was a subject with family history of Alzheimer’s disease and the difference was in bicoherence, not biphase.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Shear tests of hollow flange channel beams with stiffened web openings

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. The LSBs are commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. Shear tests of LSBs with web openings have shown that there is up to a 60% reduction in the shear capacity due to the inclusion of web openings. Hence there is a need to improve the shear capacity of LSBs with web openings. A cost effective way to eliminate the shear capacity reduction is to attach suitable stiffeners around the web openings. Hence experimental studies were undertaken to investigate the shear behaviour and strength of LSBs with stiffened web openings. In this research, various stiffening methods using plate and LSB stiffeners attached to LSBs using both welding and screw-fastening were attempted. Our test results showed that the stiffening arrangements recommended by past research for cold-formed steel channel beams are not adequate to restore the shear strengths of LSBs with web openings. Therefore new stiffener arrangements were proposed for LSBs with web openings. This paper presents the details of this experimental study and the results including the details of the optimum stiffener details for LiteSteel beams.

Shear strength of hollow flange channel beams with stiffened web openings

This LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. The LSBs are commonly used as floor joists and bearers with web openings in buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. Shear tests of LSBs with web openings have shown that there is up to 60% reduction in the shear capacity. Hence there is a need to improve the shear capacity of LSBs with web openings. A cost effective way to eliminate the shear capacity reduction is to stiffen the web openings using suitable stiffeners. Hence numerical studies were undertaken to investigate the shear capacity of LSBs with stiffened web openings. In this research, finite element models of LSBs with stiffened web openings in shear were developed to simulate the shear behaviour and strength of LSBs. Various stiffening methods using plate and LSB stiffeners attached to LSBs using both welding and screw-fastening were attempted. The developed models were then validated by comparing their results with experimental results and used in further studies. Both finite element and experimental results showed that the stiffening arrangements recommended by past research for cold-formed steel channel beams are not adequate to restore the shear strengths of LSBs with web openings. Therefore new stiffener arrangements were proposed for LSBs with web openings. This paper presents the details of this research project using numerical studies and the results.

Finite element analyses of lipped channel beams with Web openings in shear

Cold-formed steel members are increasingly used as primary structural elements in buildings due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. Shear behaviour of LCBs with web openings is more complicated and their shear capacities are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs with web openings. Finite element models of simply supported LCBs with aspect ratios of 1.0 and 1.5 were considered under a mid-span load. They were then validated by comparing their results with test results and used in a detailed parametric study. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs with web openings. Improved design equations were therefore proposed for the shear strength of LCBs with web openings. This paper presents the details of this numerical study of LCBs with web openings, and the results.

On the oscillatory behavior of transient Rayleigh Benard convection of air for 2D channel flow at moderate Rayleigh numbers

Unsteady numerical simulation of Rayleigh Benard convection heat transfer from a 2D channel is performed. The oscillatory behavior is attributed to recirculation of ascending and descending flows towards the core of the channel producing organized rolled motions. Variation of the parameters such as Reynolds number, channel outlet flow area and inclination of the channel are considered. Increasing Reynolds number (for a fixed Rayleigh number), delays the generation of vortices. The reduction in the outflow area leads to the later and the less vortex generation. As the time progresses, more vortices are generated, but the reinforced mean velocity does not let the eddies to enter the core of the channel. Therefore, they attach to the wall and reduce the heat transfer area. The inclination of the channel (both positive and negative) induces the generated vortices to get closer to each other and make an enlarged vortex.

Shear tests of lipped channel beams with stiffened web openings

Cold-formed steel lipped channel beams (LCB) are used extensively in residential, industrial and commercial buildings as load bearing structural elements. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. Past research has shown that the shear capacities of LCBs were reduced by up to 70% due to the inclusion of these web openings. Hence there is a need to improve the shear capacities of LCBs with web openings. A cost effective way of eliminating the detrimental effects of large web openings is to attach suitable stiffeners around the web openings and restore the original shear strength and stiffness of the LCBs. Hence detailed experimental studies were undertaken to investigate the shear behaviour and strength of LCBs with stiffened web openings. Both plate and stud stiffeners with varying sizes and thicknesses were attached to the web elements of LCBs using different screw-fastening arrangements. Simply supported test specimens of LCBs with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. Test results showed that the plate stiffeners established using AISI recommendations are inadequate to restore the shear strengths of LCBs with web openings. Hence new stiffener arrangements have been proposed for LCBs based on experimental results. This paper presents the details of this experimental study on the shear strength of lipped channel beams with stiffened web openings, and the results.