Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

We study the dynamical behaviors of two types of spiral-and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling G(j) and (2) the number N-f of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) G(j) is large or (b) the maximum possible number of fibroblasts per myocyte N-f(max) is large. We also observe that the minimum value of G(j), for the transition from the ST to the RS state, decreases as N-f(max) increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) G(j) increases, with fixed N-f(max), and (2) N-f(max) increases, with fixed G(j). We obtain the boundary between ST and RS stability regions in the N-f(max)-G(j) plane. In particular, for low values of N-f(max), the value of G(j), at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N-f(max) increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral-and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

On some new mathematical models for infective diseases: analysis, equilibrium, positivity and vaccination controls

196 p.

Mathematical models for the prediction of temperature distributions resulting from the discharge of heated water into large bodies of water

Mathematical models for heated water outfalls were developed for three flow regions. Near the source, the subsurface discharge into a stratified ambient water issuing from a row of buoyant jets was solved with the jet interference included in the analysis. The analysis of the flow zone close to and at intermediate distances from a surface buoyant jet was developed for the two-dimensional and axisymmetric cases. Far away from the source, a passive dispersion model was solved for a two dimensional situation taking into consideration the effects of shear current and vertical changes in diffusivity. A significant result from the surface buoyant jet analysis is the ability to predict the onset and location of an internal hydraulic jump. Prediction can be made simply from the knowledge of the source Froude number and a dimensionless surface exchange coefficient. Parametric computer programs of the above models are also developed as a part of this study. This report was submitted in fulfillment of Contract No. 14-12-570 under the sponsorship of the Federal Water Quality Administration.

Solving problems in production scheduling

Traditionally, production scheduling has been viewed as a problem-solving task that involves a single problem - generation of a suitable schedule. This paper presents an alternative model in which individual difficulties are viewed as problems, and the task is to maintain a suitable schedule by resolving as many of these problems as possible. Decision support software is described that has facilities for defining policies to handle numerous minor problems and complete problem-solving strategies to deal with major problems. The paper then discusses the potential for this style of decision support to improve the performance of human schedulers. © 1995.

Discussion on the basic mathematical models of neurons - Double synaptic weight neuron in general-purpose neurocomputer, theory and application

Based on the introduction of the traditional mathematical models of neurons in general-purpose neurocomputer, a novel all-purpose mathematical model-Double synaptic weight neuron (DSWN) is presented, which can simulate all kinds of neuron architectures, including Radial-Basis-Function (RBF) and Back-propagation (BP) models, etc. At the same time, this new model is realized using hardware and implemented in the new CASSANN-II neurocomputer that can be used to form various types of neural networks with multiple mathematical models of neurons. In this paper, the flexibility of the new model has also been described in constructing neural networks and based on the theory of Biomimetic pattern recognition (BPR) and high-dimensional space covering, a recognition system of omni directionally oriented rigid objects on the horizontal surface and a face recognition system had been implemented on CASSANN-H neurocomputer. The result showed DSWN neural network has great potential in pattern recognition.

Using mathematical models to predict the development of aircraft cabin fires

Computer based mathematical models describing aircraft fire have a role to play in the design and development of safer aircraft, in the implementation of safer and more rigorous certification criteria and in post mortuum accident investigation. As the cost involved in performing large-scale fire experiments for the next generation 'Ultra High Capacity Aircraft' (UHCA) are expected to be prohibitively high, the development and use of these modelling tools may become essential if these aircraft are to prove a safe and viable reality. By describing the present capabilities and limitations of aircraft fire models, this paper will examine the future development of these models in the areas of large scale applications through parallel computing, combustion modelling and extinguishment modelling.

Demonstration thermo-electric and MHD mathematical models of a 500 kA A1 electrolysis cell

In the present study, a 3D full cell quarter thermo-electric model of a 500kA demonstration cell has been developed and solved. In parallel, a non-linear wave MHD model of the same 500 kA demonstration cell has been developed and solved. A preliminary study of the impact of the interactions between the cell thermo-electric and MHD models will be presented.

Analysis of Degradation Data of Poly(L-lactide-co-L,D-lactic actide) and Poly(L-lactide) Obtained at Elevated and Physiological Temperatures Using Mathematical Models

The degradation of resorbable polymeric devices often takes months to years. Accelerated testing at elevated temperatures is an attractive but controversial technique. The purposes of this paper include: (a) to provide a summary of the mathematical models required to analyse accelerated degradation data and to indicate the pitfalls of using these models; (b) to improve the model previously developed by Han and Pan; (c) to provide a simple version of the model of Han and Pan with an analytical solution that is convenient to use; (d) to demonstrate the application of the improved model in two different poly(lactic acid) systems. It is shown that the simple analytical relations between molecular weight and degradation time widely used in the literature can lead to inadequate conclusions. In more general situations the rate equations are only part of a complete degradation model. Together with previous works in the literature, our study calls for care in using the accelerated testing technique.