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PubMed2001

Analysis of nonlinear dynamics on arbitrary geometries with the Virtual Cell.

The Virtual Cell is a modeling tool that allows biologists and theorists alike to specify and simulate cell-biophysical models on arbitrarily complex geometries. The framework combines an intuitive, front-end graphical user interface that runs in a web browser, sophisticated server-side numerical algorithms, a database for storage of models and simulation results, and flexible visualization capabilities. In this paper, we present an overview of the capabilities of the Virtual Cell, and, for the first time, the detailed mathematical formulation used as the basis for spatial computations. We also present summaries of two rather typical modeling projects, in order to illustrate the principal capabilities of the Virtual Cell. (c) 2001 American Institute of Physics.

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PubMed2002

Progress toward controlling in vivo fibrillating sheep atria using a nonlinear-dynamics-based closed-loop feedback method.

We describe preliminary experiments on controlling in vivo atrial fibrillation using a closed-loop feedback protocol that measures the dynamics of the right atrium at a single spatial location and applies control perturbations at a single spatial location. This study allows investigation of control of cardiac dynamics in a preparation that is physiologically close to an in vivo human heart. The spatial-temporal response of the fibrillating sheep atrium is measured using a multi-channel electronic recording system to assess the control effectiveness. In an attempt to suppress fibrillation, we implement a scheme that paces occasionally the cardiac muscle with small shocks. When successful, the inter-activation time interval is the same and electrical stimuli are only applied when the controller senses that the dynamics are beginning to depart from the desired periodic rhythm. The shock timing is adjusted in real time using a control algorithm that attempts to synchronize the most recently measured inter-activation interval with the previous interval by inducing an activation at a time projected by the algorithm. The scheme is "single-sided" in that it can only shorten the inter-activation time but not lengthen it. Using probability distributions of the inter-activation time intervals, we find that the feedback protocol is not effective in regularizing the dynamics. One possible reason for the less-than-successful results is that the controller often attempts to stimulate the tissue while it is still in the refractory state and hence it does not induce an activation. (c) 2002 American Institute of Physics.

Journal Article↗
PubMed1995

Nonlinear dynamical analysis of turbulence in a stable cloud layer.

An eight mode truncated spectral model based on Burgers' approximation to the one-dimensional Navier-Stokes equations is used to compute the Lyapunov dimension of the dynamical attractor for turbulence in a stable cloud layer. The model results are compared with the correlation dimension obtained earlier from a time series of radar Doppler and reflectivity signals from a turbulent layer in a marine stratus cloud. The analysis supports a weak coupling explanation for the lower correlation dimension found for the reflectivity time series compared with that for the Doppler time series. Turbulent Prandtl number emerges from the analysis as a flow parameter which can enlarge the dimension of the model's dynamical attractor, but the attractor dimension computed for the model remains lower than the radar Doppler correlation dimension. Linear stability analysis of the model's equilibrium states suggests that a nontruncated version of the model will possess an attractor which is also of lower dimension than the radar Doppler correlation dimension. (c) 1995 American Institute of Physics.

Journal Article↗
PubMed2003

Analysis of the nonlinear dynamics of daily broiler growth and feed intake.

Daily BW velocity (BWV) and acceleration (BWA) of individual birds have been demonstrated to be oscillatory. Daily feed intake velocity (FIV) and acceleration (FIA) were hypothesized to be oscillatory and to have a positive relationship with BWV and BWA, respectively. Forty-eight male broiler chicks were individually caged and provided a commercial starter feed ad libitum for 49 d. BW and feed intake (FI) were measured daily. Experiment 1 confirmed that, on a daily basis, BWV, BWA, FIV, and FIA were oscillatory. There was a positive correlation between BW and FI, BWV and FIV, and BWA and FIA. A Kohonen neural network (KNN) clustered BWV and FIV into two and three sequential phases. BWA and FIA analysis did not make definitive clusters. In experiment 2, it was hypothesized that correlation between BWV and FIV would increase with feeding of grower and finisher rations. It was hypothesized that KNN three phase clusters may provide more biologically ideal times of ration change (TORC) for starter, grower, and finisher rations. For 49 d, five treatments, nine birds per treatment, were fed starter, grower, and finisher rations singly or together with dietary changes according to an industry or KNN-determined TORC. Evaluation was made of BW, FI, and carcass characteristics. No significant mean differences were found. Compared to the industry group, the KNN group demonstrated significantly improved uniformity (i.e., smaller SD) of BW (bled out), FI, dressing percentage, and some of the carcass characteristics. Differences between KNN and industry TORC results might have been related to the length of time the birds were fed the starter, grower, and finisher diets.

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