A model of heart rate kinetics in response to exercise

We present a mathematical model, in the form of two coupled ordinary differential equations, for the heart rate kinetics in response to exercise. Our heart rate model is an adaptation of the model of oxygen uptake kinetics of Stirling: a physiological justification for this adaptation, as well as the physiological basis of our heart rate model is provided. We also present the optimal fit of the heart rate model to a set of raw un averaged data for multiple constant intensity exercises for an individual at a particular level of fitness

Dilation kinetics of glassy, aromatic polyimides induced by carbon dioxide sorption

Over the past years, the equilibrium sorption of gases in polymers has been intensively studied. Mostly, glassy polymers were investigated because of their excellent selective mass transport properties. This work does not focus on the equilibrium sorption but on the kinetics to reach the equilibrium. We developed a new experimental method measuring the sorption-induced dilation kinetics of a polymer film. Carbon dioxide and glassy, aromatic polyimides were chosen as model systems. Low-pressure experiments demonstrate that the measured dilation kinetics represent the sorption kinetics. A significant delay between the sorption and dilation kinetics is based on the fact that dilation kinetics occurs simultaneously with the concentration increase in the center of the polymer film. High-pressure experiments reveal significant differences in dilation kinetics compared to low-pressure experiments. Generally, three regimes can be distinguished in the dilation kinetics: a first, fast volume increase followed by two much slower regimes of volume increase. The magnitude of fast and slow dilation kinetics strongly depends on the swelling history of the polymer sample. The results of the experiments are analyzed in the light of a model relating the fast dilation kinetics to a reversible Fickian dilation and the slower dilation kinetics to an irreversible, relaxational dilation

Aggregation kinetics in a model colloidal suspension

We present molecular dynamics simulations of aggregation kinetics in a colloidal suspension modeled as a highly asymmetric binary mixture. Starting from a configuration with largely uncorrelated colloidal particles the system relaxes by coagulation-fragmentation dynamics to a structured state of low-dimensionality clusters with an exponential size distribution. The results show that short-range repulsive interactions alone can give rise to so-called cluster phases. For the present model and probably other, more common colloids, the observed clusters appear to be equilibrium phase fluctuations induced by the entropic inter-colloidal attractions

Predicting protein decomposition: the case of aspartic-acid racemization kinetics

The increase in proportion of the non-biological (D-) isomer of aspartic acid (Asp) relative to the L- isomer has been widely used in archaeology and geochemistry as a tool for dating. The method has proved controversial, particularly when used for bones. The non-linear kinetics of Asp racemization have prompted a number of suggestions as to the underlying mechanism(s) and have led to the use of mathe- matical transformations which linearize the increase in D-Asp with respect to time. Using one example, a suggestion that the initial rapid phase of Asp racemization is due to a contribution from asparagine (Asn), we demonstrate how a simple model of the degradation and racemization of Asn can be used to predict the observed kinetics. A more complex model of peptide bound Asx (Asn+Asp) racemization, which occurs via the formation of a cyclic succinimide (Asu), can be used to correctly predict Asx racemi- zation kinetics in proteins at high temperatures (95-140 °C). The model fails to predict racemization kinetics in dentine collagen at 37 °C. The reason for this is that Asu formation is highly conformation dependent and is predicted to occur extremely slowly in triple helical collagen. As conformation strongly in£uences the rate of Asu formation and hence Asx racemization, the use of extrapolation from high temperatures to estimate racemization kinetics of Asx in proteins below their denaturation temperature is called into question. In the case of archaeological bone, we argue that the D:L ratio of Asx re£ects the proportion of non- helical to helical collagen, overlain by the e¡ects of leaching of more soluble (and conformationally unconstrained) peptides. Thus, racemization kinetics in bone are potentially unpredictable, and the proposed use of Asx racemization to estimate the extent of DNA depurination in archaeological bones is challenged

Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together.Comment: 18 pages, 11 figures, published in Physical Review E 74, 041904 (2006

Kinetics of the low-temperature pyrolysis of polyethene, polypropene and polystyrene modeling, experimental determination and comparison with literature models and data

The pyrolysis kinetics of low-density polyethylene, high-density polyethylene, polypropylene, and polystyrene has been studied at temperatures below 450 C. In addition, a literature review on the low-temperature pyrolysis of these polymers has been conducted and has revealed that the scatter in the reported kinetic data is significant, which is most probably due to the use of simple first-order kinetic models to interpret the experimental data. This model type is only applicable in a small conversion range, but was used by many authors over a much wider conversion range. In this investigation the pyrolysis kinetics of the forementioned polymers and a mixture of polymers has been studied at temperatures below 450 C by performing isothermal thermogravimetric analysis (TGA) experiments. The TGA experimental data was used to determine the kinetic parameters on the basis of a simple first-order model for high conversions (70-90%) and a model developed in the present study, termed the random chain dissociation (RCD) model, for the entire conversion range. The influence of important parameters, such as molecular weight, extent of branching and -scission on the pyrolysis kinetics was studied with the RCD model. This model was also used to calculate the primary product spectrum of the pyrolysis process. The effect of the extent of branching and the initial molecular weight on the pyrolysis process was also studied experimentally. The effect of the extent of branching was found to be quite significant, but the effect of the initial molecular weight was minor. These results were found to agree quite well with the predictions obtained from the RCD model. Finally, the behavior of mixtures of the aforementioned polymers was studied and it was found that the pyrolysis kinetics of the polymers in the mixture remains unaltered in comparison with the pyrolysis kinetics of the pure polymers