The Pathway for Oxygen: Tutorial Modelling on Oxygen Transport from Air to Mitochondrion: The Pathway for Oxygen.

The 'Pathway for Oxygen' is captured in a set of models describing quantitative relationships between fluxes and driving forces for the flux of oxygen from the external air source to the mitochondrial sink at cytochrome oxidase. The intervening processes involve convection, membrane permeation, diffusion of free and heme-bound O2 and enzymatic reactions. While this system's basic elements are simple: ventilation, alveolar gas exchange with blood, circulation of the blood, perfusion of an organ, uptake by tissue, and consumption by chemical reaction, integration of these pieces quickly becomes complex.

Semi-automated Modular Program Constructor for physiological modeling: Building cell and organ models.

The Modular Program Constructor (MPC) is an open-source Java based modeling utility, built upon JSim's Mathematical Modeling Language (MML) ( http://www.physiome.org/jsim/) that uses directives embedded in model code to construct larger, more complicated models quickly and with less error than manually combining models.

JSim, an open-source modeling system for data analysis.

JSim is a simulation system for developing models, designing experiments, and evaluating hypotheses on physiological and pharmacological systems through the testing of model solutions against data. It is designed for interactive, iterative manipulation of the model code, handling of multiple data sets and parameter sets, and for making comparisons among different models running simultaneously or separately. Interactive use is supported by a large collection of graphical user interfaces for model writing and compilation diagnostics, defining input functions, model runs, selection of algorithms solving ordinary and partial differential equations, run-time multidimensional graphics, parameter optimization (8 methods), sensitivity analysis, and Monte Carlo simulation for defining confidence ranges.

Compartmental modeling in the analysis of biological systems.

Compartmental models are composed of sets of interconnected mixing chambers or stirred tanks. Each component of the system is considered to be homogeneous, instantly mixed, with uniform concentration. The state variables are concentrations or molar amounts of chemical species.

Multiscale modeling of metabolism, flows, and exchanges in heterogeneous organs.

Large-scale models accounting for the processes supporting metabolism and function in an organ or tissue with a marked heterogeneity of flows and metabolic rates are computationally complex and tedious to compute. Their use in the analysis of data from positron emission tomography (PET) and magnetic resonance imaging (MRI) requires model reduction since the data are composed of concentration-time curves from hundreds of regions of interest (ROI) within the organ. Within each ROI, one must account for blood flow, intracapillary gradients in concentrations, transmembrane transport, and intracellular reactions.

Modeling oxygen and carbon dioxide transport and exchange using a closed loop circulatory system.

The binding and buffering of O2 and CO2 in the blood influence their exchange in lung and tissues and their transport through the circulation. To investigate the binding and buffering effects, a model of blood-tissue gas exchange is used. The model accounts for hemoglobin saturation, the simultaneous binding of O2, CO2, H+, 2,3-DPG to hemoglobin, and temperature effects.

GENTEX, a general multiscale model for in vivo tissue exchanges and intraorgan metabolism.

Endothelial cells lining myocardial capillaries not only impede transport of blood solutes to the contractile cells, but also take up and release substrates, competing with myocytes. Solutes permeating this barrier exhibit concentration gradients along the capillary. This paper introduces a generic model, GENTEX, to characterize blood-tissue exchanges.

Deriving dispersional and scaled windowed variance analyses using the correlation function of discrete fractional Gaussian noise.

Methods for estimating the fractal dimension, D, or the related Hurst coefficient, H, for a one-dimensional fractal series include Hurst's method of rescaled range analysis, spectral analysis, dispersional analysis, and scaled windowed variance analysis (which is related to detrended fluctuation analysis). Dispersional analysis estimates H by using the variance of the grouped means of discrete fractional Gaussian noise series (DfGn). Scaled windowed variance analysis estimates H using the mean of grouped variances of discrete fractional Brownian motion (DfBm) series.

On two-dimensional fractional Brownian motion and fractional Brownian random field.

As a generalization of one-dimensional fractional Brownian motion (1dfBm), we introduce a class of two-dimensional, self-similar, strongly correlated random walks whose variance scales with power law N(2) (H) (0 < H < 1). We report analytical results on the statistical size and shape, and segment distribution of its trajectory in the limit of large N. The relevance of these results to polymer theory is discussed.

Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series.

Three-scaled windowed variance methods (standard, linear regression detrended, and brdge detrended) for estimating the Hurst coefficient (H) are evaluated. The Hurst coefficient, with 0 < H < 1, characterizes self-similar decay in the time-series autocorrelation function. The scaled windowed variance methods estimate H for fractional Brownian motion (fBm) signals which are cumulative sums of fractional Gaussian noise (fGn) signals.