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At least 793 records · Page 44Linked to original sources
PubMed1983

A practical approach to the hepatobiliary kinetics of 99mTc-HIDA. Clinical validation of the method and a preliminary report on its use for parametric imaging.

99mTc-diethyl-HIDA cholescintigraphy was performed on 24 patients with histologically proven liver disease and on 10 normal adult subjects. Liver mass transport of HIDA was interpreted with the aid of a probabilistic model, assuming that the tracer particles undergo mixed random walks with drifts. The radiohepatograms were thus fitted with a gamma-variate function and the fitting parameters were evaluated as estimates of the severity of the disease. These parameters, together with the transit times, were also used to generate parametric images of liver function. The advantages of this approach are discussed and the following conclusions are drawn: (1) The gamma-fit is highly satisfactory with any type of experimental curve (0.98 less than r less than 1). (2) The parameters derived from the gamma-fit make it possible to objectively assess the extent of liver functional impairment. (3) Parametric imaging of the liver mass transport of HIDA is easily implemented, but still more experience is needed to assess its impact on patient care.

Bile Ducts↗
PubMed1985

A model for the lateral diffusion of "stiff" chains in a lipid bilayer.

We present random walk models for the diffusive motion of lipid probe molecules in a lipid bilayer and calculate the diffusion constants for probes spanning the entire bilayer and for probes extending through one lipid layer only. The "stiffness" of such molecules can explain the observed value of 2/3 for the ratio of these diffusion constants.

Diffusion↗
PubMed1989

The problem of our common mitochondrial mother.

It has been suggested that the mitochondrial DNA (mtDNA) of all present-day human beings stems exclusively from one woman who lived about 200000 years ago in Africa; examination of the problem by the mathematical theory of random walks supposedly renders alternatives very unlikely. However, a statistical argument first used by Fisher indicates that this hypothesis is untenable, at least if the assumptions made by previous workers are accepted. All present-day mtDNA might go back to one individual, especially if small populations and population bottlenecks with very small numbers of reproducing individuals are assumed; nevertheless, this phase in the evolution of Homo sapiens probably dates back considerably more than 200000 years.

Biological Evolution↗
PubMed1987

Limit theorems for the population size of a birth and death process allowing catastrophes.

The linear birth and death process with catastrophes is formulated as a right continuous random walk on the non-negative integers which evolves in continuous time with an instantaneous jump rate proportional to the current value of the process. It is shown that distributions of the population size can be represented in terms of those of a certain Markov branching process. The ergodic theory of Markov branching process transition probabilities is then used to develop a fairly complete understanding of the behaviour of the population size of the birth-death-catastrophe process.

Animals↗
PubMed1983

Use of gamma distributed residence times in pharmacokinetics.

Using a nonclassical statistically based pharmacokinetic concept, a theory is presented which can be applied to the analysis of concentration-time data fitted by power functions of time C = At-ae-bt, which is shown to be equivalent to the assumption of gamma distributed residence times of drugs. The shape and scale parameters a and b, respectively, are interpreted physiologically in terms of a recirculatory model. It is shown how the shape parameter a, which is only dependent on the coefficient of variation of residence times, is affected by the processes of drug distribution and elimination. The time course of the blood concentration following multiple doses and continuous infusion is predicted for gamma-like drug disposition curves. The assumption of gamma distributed disposition residence times is theoretically based on a random walk model of circulatory drug transport, and the conditions are investigated under which gamma curves can be empirically fitted to oral concentration-time data. The parameters of concentration-time profiles following solid dosage forms, for example, are explained by the means and coefficients of variation of the disposition residence time and dissolution time distribution, respectively. The advantages of this concept compared to the conventional method of fitting sums of exponentials to the data are described.

Administration, Oral↗
PubMed1996

The dynamical theory of coevolution: a derivation from stochastic ecological processes.

In this paper we develop a dynamical theory of coevolution in ecological communities. The derivation explicitly accounts for the stochastic components of evolutionary change and is based on ecological processes at the level of the individual. We show that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space. A quantitative description of this stochastic process in terms of a master equation is derived. By determining the first jump moment of this process we abstract the dynamic of the mean evolutionary path. To first order the resulting equation coincides with a dynamic that has frequently been assumed in evolutionary game theory. Apart from recovering this canonical equation we systematically establish the underlying assumptions. We provide higher order corrections and show that these can give rise to new, unexpected evolutionary effects including shifting evolutionary isoclines and evolutionary slowing down of mean paths as they approach evolutionary equilibria. Extensions of the derivation to more general ecological settings are discussed. In particular we allow for multi-trait coevolution and analyze coevolution under nonequilibrium population dynamics.

Animals↗
PubMed1997

A two-backbone polymer model for interphase chromosome geometry.

A polymer model for the overall geometric structure of a human chromosome during the G0/G1 portion of cell-cycle interphase is constructed, based on fluorescence in situ hybridization data on distances between defined genomic sequences. The model consists of flexible giant loops, averaging about 6 million base pairs, with two random-walk backbones; it involves essentially three parameters. Numerical results based on properly selected values of parameters fit the data well.

Chromosomes, Human↗
PubMedDate not supplied

Noncompartmental models of whole-body clearance of tracers: a review.

Noncompartmental models are defined as models that allow for transport of material through regions of the body that are not necessarily well-mixed or of uniform concentration. The clearance of a substance of interest (metabolite or drug) from a noncompartmental system will not necessarily be governed by a sum of exponentials or even be describable by a set of ordinary differential equations. The model may involve diffusion or other random walk processes, leading to the solution in terms of the partial differential equation of diffusion or in terms of probability distributions. It may use the theory of linear systems to obviate the need for defining any precise anatomical structure. A number of the models reviewed deal with plasma clearance curves that are best described by power functions of time. Circulatory models are reviewed from their inception to the present. Recent studies on clearance as a fractal process are introduced.

Animals↗
PubMed2001

Mathematical models of eye movements in reading: a possible role for autonomous saccades.

An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory - almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes.

Algorithms↗
PubMed2003

Simulations of NMR-detected diffusion in suspensions of red cells: the effects of variation in membrane permeability and observation time.

Monte Carlo random-walk simulations of diffusion in virtual lattices of cells have been used to study and characterize diffusion-coherence phenomena that arise when pulsed field-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) experiments are conducted on human red blood cell (RBC; erythrocytes) suspensions. These coherence effects are manifest as diffraction-like patterns when the normalized PGSE signal intensities are plotted as a function of the spatial wave vector q in so-called q-space plots. q-Space analysis is sensitive to small changes in cell morphology, cell size, membrane transport rates, hematocrit, and packing arrangement. In the present study we used simulations to predict the effect of varying the time over which diffusion is measured (the "observation time" or "diffusion time") and the permeability of the membrane on the form of q-space plots. Thus we predict that inhibiting water exchange across the human RBC membrane, such that the value of the permeability coefficient is reduced by approximately an order of magnitude below the normal physiological value, will effectively render the membrane impermeable on the timescale of the PGSE NMR experiment; further inhibition will therefore result in negligible reduction in the measured root-mean-square displacement (r.m.s.d.) of diffusing water as a function of the observation time. The work also underscores the importance of using an appropriate experimental observation time if q-space data are to be used to estimate compartment dimensions and interbarrier spacing, and illustrates an expeditious method for determining this value.

Biophysics↗
PubMed2000

Mean residence time of molecules diffusing in a cell bounded by a semi-permeable membrane: Monte Carlo simulations and an expression relating membrane transition probability to permeability.

The rapid exchange of water across erythrocyte membranes is readily measured using an NMR method that entails doping a suspension of cells with a moderately high concentration of Mn(2-) and measuring the rate of transverse relaxation of the nuclear magnetisation. Analysis of the data yields an estimate of the rate constant for membrane transport, from which the membrane permeability can be determined. It is assumed in the analysis that the efflux rate of the water is solely a function of the rate of membrane permeation and that the time it takes for intracellular water molecules to diffuse to the membrane is relatively insignificant. The limits of this assumption were explored by using random-walk simulations of diffusion in cells modelled as parallel planes, spheres, and biconcave discs. The rate of membrane transport was specified in terms of a transition probability but it was not initially clear what the relationship should be between this parameter and the diffusional membrane permeability P(d). This relationship was derived and used to show that the mean residence time for a water molecule is determined by P(d) when the diffusion coefficient is above a certain threshold value; it is determined by the distance to the membrane below that value.

Animals↗
PubMed2001

Dictyostelium cells' cytoplasm as an active viscoplastic body.

We applied a recently developed microrheology technique based on colloidal magnetic tweezers to measure local viscoelastic moduli and active forces in cells of Dictyostelium discoideum. The active transport of nonmagnetic beads taken up by phagocytosis was analyzed by single particle tracking, which allowed us to measure the length of straight steps and the corresponding velocities of the movements. The motion consists of a superposition of nearly straight long-range steps (step length in the micrometer range) and local random walks (step widths about 0.1 microm). The velocities for the former type of motion range from 1 to 3 microm/s. They decrease with increasing bead size and are attributed to rapid active transport along microtubuli. The short-range local motions exhibit velocities of less than 0.5 microm/s and reflect the internal dynamics of the cytoplasm. Viscoelastic response curves were measured by application of force pulses with amplitudes varying between 50 pN and 400 pN. Analysis of the response curves in terms of mechanical equivalent circuits yielded cytoplasmic viscosities varying between 10 and 350 Pa s. Simultaneous analysis of the response curves and of the bead trajectories showed that the motion of the beads is determined by the local yield stress within the cytoplasmic scaffold and cisternae, which varies between sigma = 30 Pa and 250 Pa. The motion of intracellular particles is interpreted in terms of viscoplastic behavior and the apparent viscosity is a measure of the reciprocal rate of bond breakage within the cytoplasmatic network. The viscoelastic moduli are interpreted as dynamic quantities which depend sensitively on the amplitude of the forces, and the rate of bond breakage is determined by the Arrhenius-Kramers law with the activation energy being reduced by the work performed by the applied force. In agreement with previous work, we provide evidence that the myosin II-deficient cells exhibit higher yield stresses, suggesting that the function of myosin II as a cross-linker is taken over by the other (non-active) cross-linkers.

Animals↗
PubMed2006

M5 mesoscopic and macroscopic models for mesenchymal motion.

In this paper mesoscopic (individual based) and macroscopic (population based) models for mesenchymal motion of cells in fibre networks are developed. Mesenchymal motion is a form of cellular movement that occurs in three-dimensions through tissues formed from fibre networks, for example the invasion of tumor metastases through collagen networks. The movement of cells is guided by the directionality of the network and in addition, the network is degraded by proteases. The main results of this paper are derivations of mesoscopic and macroscopic models for mesenchymal motion in a timely varying network tissue. The mesoscopic model is based on a transport equation for correlated random walk and the macroscopic model has the form of a drift-diffusion equation where the mean drift velocity is given by the mean orientation of the tissue and the diffusion tensor is given by the variance-covariance matrix of the tissue orientations. The transport equation as well as the drift-diffusion limit are coupled to a differential equation that describes the tissue changes explicitly, where we distinguish the cases of directed and undirected tissues. As a result the drift velocity and the diffusion tensor are timely varying. We discuss relations to existing models and possible applications.

Algorithms↗
PubMed2001

Mathematical modeling of the onset of capillary formation initiating angiogenesis.

It is well accepted that neo-vascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In this paper we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In this model, a single layer of endothelial cells is separated by a vascular wall from an extracellular tissue matrix. A coupled system of ordinary and partial differential equations is derived which, in the presence of an angiogenic agent, predicts the aggregation of the endothelial cells and the collapse of the vascular lamina, opening a passage into the extracellular matrix. We refer to this as the onset of vascular sprouting. Some biological evidence for the correctness of our model is indicated by the formation of teats in utero. Further evidence for the correctness of the model is given by its prediction that endothelial cells will line the nascent capillary at the onset of capillary angiogenesis.

Angiogenesis Inducing Agents↗
PubMed2001

Migration of fallout-radionuclides in the soil: effect of non-uniformity of the sorption properties on the activity-depth profiles.

Experimentally observed activity-depth profiles of fallout radionuclides in the soil frequently exhibit a comparatively fast moving tail in soil layers below the peak concentration (tailing). Monte Carlo calculations on the basis of the convection-dispersion model show that this phenomenon can be explained by assuming that either the hydraulic properties of the soil (characterised by the diffusion/dispersion coefficient and pore water velocity) or the sorption properties of the soil (characterised by the distribution coefficient Kd), or both, exhibit a horizontal variability according to a log-normal distribution. Modifications of the activity-depth profile due to a Kd value which decreases linearly with depth were examined by using a random walk approach, based also on the convection-dispersion model. In this case, however, a pronounced tailing effect of the activity-depth profile did not result. Interpretation and realistic modelling of an experimentally observed activity-depth profile which exhibits a tailing effect is thus not unambiguously possible without any additional information on the spatial variability of the hydraulic parameters and, independently, also for the sorption properties.

Absorption↗
PubMed2005

Comparing internal models of the dynamics of the visual environment.

It is well known that the human postural control system responds to motion of the visual scene, but the implicit assumptions it makes about the visual environment and what quantities, if any, it estimates about the visual environment are unknown. This study compares the behavior of four models of the human postural control system to experimental data. Three include internal models that estimate the state of the visual environment, implicitly assuming its dynamics to be that of a linear stochastic process (respectively, a random walk, a general first-order process, and a general second-order process). In each case, all of the coefficients that describe the process are estimated by an adaptive scheme based on maximum likelihood. The fourth model does not estimate the state of the visual environment. It adjusts sensory weights to minimize the mean square of the control signal without making any specific assumptions about the dynamic properties of the environmental motion. We find that both having an internal model of the visual environment and its type make a significant difference in how the postural system responds to motion of the visual scene. Notably, the second-order process model outperforms the human postural system in its response to sinusoidal stimulation. Specifically, the second-order process model can correctly identify the frequency of the stimulus and completely compensate so that the motion of the visual scene has no effect on sway. In this case the postural control system extracts the same information from the visual modality as it does when the visual scene is stationary. The fourth model that does not simulate the motion of the visual environment is the only one that reproduces the experimentally observed result that, across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases but the phase remains roughly constant. Our results suggest that the human postural control system does not estimate the state of the visual environment to respond to sinusoidal stimuli.

Algorithms↗
PubMed1997

Modeling neural activity using the generalized inverse Gaussian distribution.

Spike trains from neurons are often used to make inferences about the underlying processes that generate the spikes. Random walks or diffusions are commonly used to model these processes; in such models, a spike corresponds to the first passage of the diffusion to a boundary, or firing threshold. An important first step in such a study is to fit families of densities to the trains' interspike interval histograms; the estimated parameters, and the families' goodness of fit can then provide information about the process leading to the spikes. In this paper, we propose the generalized inverse Gaussian family because its members arise as first passage time distributions of certain diffusions to a constant boundary. We provide some theoretical support for the use of these diffusions in neural firing models. We compare this family with the lognormal family, using spike trains from retinal ganglion cells of goldfish, and simulations from an integrate-and-fire and a dynamical model for generating spikes. We show that the generalized inverse Gaussian family is closer to the true model in all these cases.

Action Potentials↗
PubMed2006

Wayfinding with words: spatial learning and navigation using dynamically updated verbal descriptions.

This work investigates whether large-scale indoor layouts can be learned and navigated non-visually, using verbal descriptions of layout geometry that are updated, e.g. contingent on a participant's location in a building. In previous research, verbal information has been used to facilitate route following, not to support free exploration and wayfinding. Our results with blindfolded-sighted participants demonstrate that accurate learning and wayfinding performance is possible using verbal descriptions and that it is sufficient to describe only local geometric detail. In addition, no differences in learning or navigation performance were observed between the verbal study and a control study using visual input. Verbal learning was also compared to the performance of a random walk model, demonstrating that human search behavior is not based on chance decision-making. However, the model performed more like human participants after adding a constraint that biased it against reversing direction.

Adolescent↗