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Biomedical subjects

James P Keener

Publications and source records attributed to James P Keener.

8 recordsLinked to original sources
PubMed2006

Fibrin gel formation in a shear flow.

Blood clots are made up of platelets and fibrin gel, and the relative amount of fibrin is strongly influenced by the shear rate. In order to explore this phenomenon, this paper presents a model of fibrin gel formation over the surface of an injured blood vessel in a shear flow. A condition for gelation including source and sink terms of polymer is derived. A simplified model of coagulation, involving activation and inhibition of the enzyme thrombin and thrombin-mediated production of fibrin monomer, is combined with the model of gelation to explore how the shear rate and other parameters control the formation of fibrin gel. The results show that the thrombin inhibition rate, the gel permeability and the shear rate are key parameters in regulating the height of the fibrin gel.

Algorithms↗
PubMed2006

Stochastic calcium oscillations.

While the oscillatory release of calcium from intracellular stores is comprised of fundamentally stochastic events, most models of calcium oscillations are deterministic. As a result, the transition to calcium oscillations as parameters, such as IP(3) concentration, are changed is not described correctly. The fundamental difficulty is that whole-cell models of calcium dynamics are based on the assumptions that the calcium concentration is spatially homogeneous, and that there are a sufficiently large number of release sites per unit volume so that the law of large numbers is applicable. For situations where these underlying assumptions are not applicable, a new modelling approach is needed. In this paper, we present a model and its analysis of calcium dynamics that incorporates the fundamental stochasticity of release events. The model is based on the assumptions that release events are rapid, while reactivation is slow. The model presented here is comprised of two parts. In the first, a stochastic version of the fire-diffuse-fire model is studied in order to understand the spark-to-wave transition and the probability of sparks resulting in abortive waves versus whole-cell calcium release. In the second, this information about the spark-to-wave transition is incorporated into a stochastic model (a Chapman-Kolmogorov equation) that tracks the number of activated and inactivated calcium release sites as a function of time. By solving this model numerically, information about the timing of whole-cell calcium release is obtained. The results of this analysis show a transition to oscillations that agrees well with data and with Monte Carlo simulations.

Calcium↗
PubMed2004

The topology of defibrillation.

We describe how Art Winfree's ideas about phase singularities can be used to understand the response of cardiac tissue with a random preexisting pattern of reentrant waves (fibrillation) to a large brief current stimulus. This discussion is organized around spatial dimension, beginning with a discussion of reentry on a periodic ring, followed by reentry in a two-dimensional planar domain (spiral waves), and ending with consideration of three-dimensional reentrant patterns (scroll waves). In all cases, we show how reentrant activity is changed by the application of a shock, describing conditions under which defibrillation is successful or not. Using topological arguments we draw the general conclusion that with a generic placement of stimulating electrodes, large-scale virtual electrodes do not give an adequate explanation for the mechanism of defibrillation.

Electric Countershock↗
PubMed2004

The role of the biofilm matrix in structural development.

Although the initiation, development and control of biofilms has been an area of experimental investigation for more than three decades, the role of extra-cellular polymeric substance (EPS) has not been well studied. We present a mathematical description of the EPS matrix to study the development of heterogeneous biofilm morphology. In developing the model, we assume that the biofilm is a biological gel composed of EPS and water. The bacteria are enmeshed in the network and are the producers of the polymer. In response to external conditions, gels absorb or expel solvent causing swelling or contraction due to osmotic pressure gradients. The physical morphology of the biofilm depends on the temperature, solvent composition, pH and ionic concentrations through osmotic pressure. This gives a physically based mechanism for the redistribution of biomass within the biofilm. Analysis of a reduced model indicates that biomass redistribution, through the mechanism of swelling, may induce the formation of isolated towers or mushroom clusters by spatial variation in EPS production which leads to gradients in osmotic pressure.

Biofilms↗
PubMed2003

The effect of spatial scale of resistive inhomogeneity on defibrillation of cardiac tissue.

Defibrillation of cardiac tissue can be viewed in the context of dynamical systems theory as the attempt to move a dynamical system from the basin of attraction of one attractor (fibrillation) to another (the uniform rest state) by applying a stimulus whose form is physically constrained. Here we give an introduction to the physical mechanism of cardiac defibrillation from this dynamical perspective and examine the role of resistive inhomogeneity on defibrillation efficacy. Using numerical simulations with rotating waves on a one-dimensional periodic ring, we study the role of the spatial scale of resistive inhomogeneity on defibrillation. For a rotating wave on a periodic ring there are three stable attractors, namely the uniform rest state, a wave traveling clockwise and a wave traveling counterclockwise. As a result, the application of a stimulus has the potential for three different outcomes, namely elimination of the wave, phase resetting of the wave, and reversal of the wave. The results presented here show that with resistive inhomogeneities of large spatial scale, all three of these transitions are possible with large amplitude shocks, so that the probability of defibrillation is bounded well below one, independent of stimulus amplitude. On the other hand, resistive inhomogeneities of small spatial scale produce a defibrillation threshold that is qualitatively consistent with that found experimentally, namely the probability of defibrillation success is an increasing function that approaches one for large enough stimulus amplitude. Extending these results to higher dimensions, we describe conditions for successful defibrillation of functional reentry with large scale spatial inhomogeneity, but find that elimination of anatomical reentry is quite difficult. With small spatial scale inhomogeneity, there are no similar restrictions.

Atrial Fibrillation↗
PubMed2003

A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia.

The response of tissue to ischemia (cessation of blood flow and deprivation of oxygen) includes swelling of the intracellular space, shrinkage of the extracellular space, and an increase in the extracellular potassium concentration. The responses of cardiac and brain tissue to ischemia are qualitatively different in that cardiac tissue shows a rise in extracellular potassium over several minutes from about 5 to 10-12 mM followed by a plateau, while brain tissue shows a similar initial rise followed by a very rapid increase in extracellular potassium to levels of 50-80 mM. During hypoxia the flow of blood (or perfusate) is maintained and, while there is a substantial efflux of potassium from cells, there is little accumulation of potassium in the interstitium. A mathematical model is proposed and studied to try to elucidate the mechanism(s) underlying the increase in extracellular potassium, and the different time courses seen in neural and cardiac tissue. The model involves a Hodgkin-Huxley-type description of transmembrane ion currents, allows for ion concentrations as well as volumes to change for both the intracellular and extracellular space, and includes coupling of damaged tissue to nearby healthy tissue. The model produces a response to ischemia much like that seen in neural tissue, and the mechanism underlying this response in the model is determined. The same mechanism is not present in cardiac ion models, and this may explain the qualitative difference in response shown in cardiac tissue.

Animals↗
PubMed2003

Model for the onset of fibrillation following coronary artery occlusion.

INTRODUCTION: It is the hypothesis of this article that the onset of fibrillation following a coronary artery occlusion is a direct consequence of the spatial inhomogeneity of chemical processes that occur following the occlusion. In particular, the localized increase of extracellular potassium and decrease of ATP availability lead to an increase of resting potential in the affected cells. This difference in potential between affected cells and normal cells drives a current, the "current of injury," which may drive oscillations in the border zone, a "border zone arrhythmia." The border zone arrhythmia may drive a "breakup instability" (related to the action potential duration restitution instability) in the surrounding tissue, leading to self-sustained fibrillation. METHODS AND RESULTS: In this article, we present a mathematical model demonstrating this transition from normal to fibrillatory dynamics, describing the general conditions under which this transition occurs and showing in a simple ionic model the way in which spatial inhomogeneity alone can initiate self-sustained reentrant activity. CONCLUSION: Using general arguments and numerical simulations with generic models of excitable media, we have demonstrated that a spatial region with an elevated resting potential surrounded by a spatial region wherein action potentials are foreshortened can drive a breakup instability, leading to the rapid initiation of a fibrillatory state.

Action Potentials↗