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PubMed2004

Dynamical effects of diffusive cell coupling on cardiac excitation and propagation: a simulation study.

Cell coupling is considered to be important for cardiac action potential propagation and arrhythmogenesis. We carried out computer simulations to investigate the effects of stimulation strength and cell-to-cell coupling on action potential duration (APD) restitution, APD alternans, and stability of reentry in models of isolated cell, one-dimensional cable, and two-dimensional tissue. Phase I formulation of the Luo and Rudy action potential model was used. We found that stronger stimulation resulted in a shallower APD restitution curve and onset of APD alternans at a faster pacing rate. Reducing diffusive coupling between cells prolonged APD. Weaker diffusive currents along the direction of propagation steepened APD restitution and caused APD alternans to occur at a slower pacing rate in tissue. Diffusive current due to curvature changed APD but had little effect on APD restitution slope and onset of instability. Heterogeneous cell coupling caused APD inhomogeneities in space. Reduction in coupling strength either uniformly or randomly had little effect on the rotation period and stability of a reentry, but random cell decoupling slowed the rotation period and, thus, stabilized the reentry, preventing it from breaking up into multiple waves. Therefore, in addition to its effects on action potential conduction velocity, diffusive cell coupling also affects APD in a rate-dependent manner, causes electrophysiological heterogeneities, and thus modulates the dynamics of cardiac excitation. These effects are brought about by the modulation of ionic current activation and inactivation.

Action Potentials↗
PubMed2004

Calcium dynamics in dendritic spines and spine motility.

A dendritic spine is an intracellular compartment in synapses of central neurons. The role of the fast twitching of spines, brought about by a transient rise of internal calcium concentration above that of the parent dendrite, has been hitherto unclear. We propose an explanation of the cause and effect of the twitching and its role in the functioning of the spine as a fast calcium compartment. Our molecular model postulates that rapid spine motility is due to the concerted contraction of calcium-binding proteins. The contraction induces a stream of cytoplasmic fluid in the direction of the dendritic shaft, thus speeding up the time course of spine calcium dynamics, relative to pure diffusion. Simulations indicate that chemical reaction rate theory at the molecular level can explain spine motility. They reveal two time periods in calcium dynamics, as measured recently by other researchers. It appears that rapid motility in dendritic spines increases the efficiency of calcium conduction to the dendrite and speeds up the emptying of the spine. This could play a major role in the induction of synaptic plasticity. A prediction of the model is that alteration of spine motility will modify the time course of calcium in the dendritic spine and could be tested experimentally.

Animals↗
PubMed1982

Surface functions during mitosis. III. Quantitative analysis of ligand-receptor movement into the cleavage furrow: diffusion vs. flow.

The surface distribution of concanavalin A (Con A) bound to cell membrane receptors varies dramatically as a function of mitotic phase. The lectin is distributed diffusely on cells labeled and observed between mid-prophase and early anaphase, whereas cells observed in late anaphase or telophase demonstrate a marked accumulation of Con A-receptor complexes over the developing cleavage furrow (Berlin, Oliver, and Walter. 1978. Cell. 15:327-341). In this report, we first use a system based on video intensification fluorescence microscopy to describe the simultaneous changes in cell shape and in lectin-receptor complex topography during progression of single cells through the mitotic cycle. The video analysis establishes that fluorescein succinyl Con A (F-S Con A)-receptor complex redistribution begins coincident with the first appearance of the cleavage furrow and is essentially complete within 2-3 min. This remarkable redistribution of surface fluorescence occurs during only a modest change in cell shape from a sphere to a belted cylinder. It reflects the translocation of complexes and not the accumulation of excess labeled membrane in the cleavage furrow: first, bound fluorescent cholera toxin which faithfully outlines the plasma membrane is not accumulated in the cleavage furrow, and, second, electron microscopy of peroxidase-Con A labeled cells undergoing cleavage shows that there is a high linear density of lectin within the furrow while Con A is virtually eliminated from the poles. The rate of surface movement of F-S Con A was quantitated by photon counting during a repetitive series of laser-excited fluorescence scans across dividing cells. Results were analyzed in terms of two alternative models of movement: a flow model in which complexes moved unidirectionally at constant velocity, and a diffusion model in which complexes could diffuse freely but were trapped at the cleavage furrow. According to these models, the observed rates of accumulation were attainable at either an effective flow velocity of approximately 1 micron/min, or an effective diffusion coefficient of approximately 10(-9) cm2/s. However, in separate experiments the lectin-receptor diffusion rate measured directly by the method of fluorescence recovery after photobleaching (FRAP) on metaphase cells was only approximately 10(-10) cm2/s. Most importantly, photobleaching experiments during the actual period of F-S Con A accumulation showed that lectin-receptor movement during cleavage occurs unidirectionally. These results rule out diffusion and make a process of oriented flow of ligand-receptor complexes the most likely mechanism for ligand-receptor accumulation in the cleavage furrow.

Animals↗
PubMed1975

Free energy and the kinetics of biochemical diagrams, including active transport.

In earlier papers on muscle contraction it was found very useful to relate the actual (not standard) free energy levels of the different states in the biochemical diagram of the myosin cross-bridge to the first-order rate constants governing transitions between these states and to the details of the conversion of ATP free energy into mechanical work. This same approach is applied here to other macromolecular biochemical systems, for example, carriers in active transport, and simple enzyme reactions. With the definition of free energy changes between states of diagram used here (and in the muscle papers), the rate constants of the diagram are firat order, the macromolecular transitions are effectively isomeric, the equilibrium constants are dimensionless, the free energy changes are directly related to first-order rate constant ratios, and the ratio of products of forward and backward rate constants around any cycle of the diagram is related to operational free energy changes (e.g. the in vivo free energy of ADP HYDROLYSIS). These general points are illustrated by means of particular arbitrary models, especially transport models. In contrast to the muscle case, the free energy conversion question in other biochemical systems can be handled at the less detailed, complete-cycle level rather than at the elementary transition level. There is a corresponding complete-cycle kinetics, with composite first-order rate constants for the different possible cycles (in both directions). An introductory stochastic treatment of cycle kinetics is included.

Adenosine Triphosphatases↗
PubMed2002

MR perfusion, diffusion and BOLD imaging of methotrexate-exposed swine brain.

PURPOSE: To evaluate the methotrexate (MTX)-exposed swine brain, functional magnetic resonance imaging (MRI), including perfusion, diffusion, and blood-oxygen-level-dependent (BOLD) contrast imaging, was used. MATERIAL AND METHODS: Juvenile pigs received either 2 x 5 g/m(2), or 5 x 2 g/m(2) MTX intravenously within one month. MRI was performed (sedative: propofol) before (14-17 kg, N = 6) and after (21-27 kg, N = 4) the MTX exposure. Also, age-matched controls (22-27 kg, N = 4) were imaged. RESULTS: After the MTX exposure, reduced (from 2%-4% to 0%-1%) or negative (-2% to -3%) BOLD responses were detected; apparent diffusion coefficient (ADC) or relative perfusion values did not change. CONCLUSION: This study suggests that MTX-related changes in the brain may be detected as changes in flow-metabolism coupling as reduced or negative response (for somatosensory activation) in the BOLD contrast MRI. The contrast agent perfusion MRI, without absolute quantification, may not show global damage in brain perfusion related to the MTX exposure in the swine model used. ADC (in one direction) may not indicate MTX-related changes in the brain.

Animals↗
PubMed1996

Simulation of cardiac activity and the ECG using a heart model with a reaction-diffusion action potential.

A computerized model of the heart for the simulation of the electrical cardiac activity is described. The cardiac cells are arranged in a three-dimensional cubic lattice and their action potential is governed by modified FitzHugh-Nagumo reaction-diffusion state equations system which exhibits properties such as oscillations, variable excitability and refractoriness. The modifications of the FitzHugh-Nagumo equations system account for asymmetric action potential regarding the fast depolarization and slow repolarization rate and for rotational anisotropic propagation. An isolated cell is tested for reproduction of the strength-duration curves and restitution. The structure basic unit cell is assigned with an individual set of control parameters that creates inhomogeneity and anisotropy to simulate the various cardiac components such as pacers, muscle cells and conduction fibers. The spatial resolution of the structure is 1 mm. The collective activity of the cells generates a realistic ECG waveform that scales the simulated temporal step unit to 0.2 msec. The effective diffusion coefficient ranges between 0.055 mm2/msec to 1 mm2/msec. The propagation velocity of the myocardial activation is calculated at normal direction to the wavefront surface and values obtained are 1.17 mm/msec at the muscle cells and 2.5 mm/msec at the main conduction fibers. An ischemia is induced to verify the capability of the model to account for abnormalities. The developed model can give an insight into the local and global complex dynamics of the heart's electrical activity in the transition from normal to abnormal myocardial activity and may help to estimate the effects of myocardial properties on the ECG rhythm.

Action Potentials↗
PubMed2003

Ion permeation through the gramicidin channel: atomically detailed modeling by the Stochastic Difference Equation.

Atomically detailed descriptions of ionic solution, membrane, and the gramicidin channel are used to compute molecular dynamics trajectories of ion permeation. The microsecond trajectories are calculated with the Stochastic Difference Equation (SDE), which provides approximate solutions to the equations of motions (with filtered high-frequency modes) of extended timescales. The relative permeations of lithium, sodium, and potassium are estimated by using a novel, kinetic cycle protocol and are compared with experiment. The transport through native gramicidin and one fluoro-valine variant is considered as well. Qualitative agreement between theory and experiment is obtained. The faster permeation rate of sodium compared to lithium is reproduced in the calculations. The calculations also reproduce the slower diffusion through a gramicidin with fluorinated valine compared to native gramicidin. The calculations are inconclusive about the relative rates of potassium and sodium. The experiment suggests that potassium permeates more quickly. We directly probe the kinetics of a biophysical process at a relevant time window without reducing the atomically detailed description of the system. The calculations were able to capture subtle balances between binding and diffusion that determine permeation rates. The same model gave the correct ordering of diffusion rates for cases in which electrostatic binding has opposite effects and must be supplemented by dynamic factors. Diffusion rates are faster when favorable electrostatic interactions of ions in the channel (compared to the solvent) are observed. Studies of a gramicidin variant suggest an opposite effect, in which permeation is faster for the less polar channel, indicating dynamic effects. Although both trends can be explained qualitatively, it is not possible to predict (before doing the SDE calculations) which factor is more important.

Computational Biology↗
PubMed2006

Breaking of translational symmetry of a traveling planar impulse in a two-dimensional two-variable reaction-diffusion model.

The stability of a planar impulse in rectangular spatial domains for a two-variable excitable reaction-diffusion system is numerically studied. The dependence of the stability on the size of the domain perpendicular to the direction of the propagation of the impulse is shown. The instability results in asymptotic stable curved impulses or an asymptotic spatiotemporal structure, which is generated similarly to the one-dimensional backfiring phenomenon.

Journal Article↗
PubMed2002

Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media.

The polarization properties of light scattered in a lateral direction from turbid media were studied. Polarization modulation and synchronous detection were used to measure, and Mueller calculus to model and derive, the degrees of surviving linear and circular polarization and the optical rotation induced by turbid samples. Polystyrene microspheres were used as scatterers in water solutions containing dissolved chiral, racemic, and achiral molecules. The preservation of circular polarization was found to exceed the linear polarization preservation for all samples examined. The optical rotation induced increased with the chiral molecule concentration only, whereas both linear and circular polarizations increased with an increase in the concentrations of chiral, racemic, and achiral molecules. This latter effect was shown to stem solely from the refractive index matching mechanism induced by the solute molecules, independent of their chiral nature.

Biophysical Phenomena↗
PubMed1997

Improved perfusion with rt-PA and hirulog in a rabbit model of embolic stroke.

We conducted a study using diffusion-weighted (DWI) and perfusion-weighted (PWI) magnetic resonance imaging (MRI) to evaluate the efficacy of thrombolysis in an embolic stroke model with recombinant tissue plasminogen activator (rt-PA) and hirulog, a novel direct-acting antithrombin. DWI can identify areas of ischemia minutes from stroke onset, while PWI identifies regions of impaired blood flow. Right internal carotid arteries of 36 rabbits were embolized using aged heterologous thrombi. Baseline DWI and PWI scans were obtained to confirm successful embolization. Four animals with no observable DWI lesion on the initial scan were excluded; therefore, a total of 32 animals were randomized to one of three treatment groups: rt-PA (n = 11), rt-PA plus hirulog (n = 11), or placebo (n = 10). Treatment was begun 1 h after stroke induction. Intravenous doses were as follows: rt-PA, 5 mg/kg over 0.5 h with 20% of the total dose given as a bolus; hirulog, 1 mg/kg bolus followed by 5 mg/kg over 1 h. MRI was performed at 2, 3, and 5 h following embolization. Six hours after embolization, brains were harvested, examined for hemorrhage, then prepared for histologic analysis. The rt-PA decreased fibrinogen levels by 73%, and hirulog prolonged the aPTT to four times the control value. Posttreatment areas of diffusion abnormality and perfusion delay were expressed as a ratio of baseline values. Significantly improved perfusion was seen in the rt-PA plus hirulog group compared with placebo (normalized ratios of the perfusion delay areas were as follows: placebo, 1.58, 0.47-3.59; rt-PA, 1.12, 0.04-3.95; rt-PA and hirulog, 0.40, 0.02-1.08; p < 0.05). Comparison of diffusion abnormality ratios measured at 5 h showed trends favoring reduced lesion size in both groups given rt-PA (normalized ratios of diffusion abnormality areas were as follows: placebo, 3.69, 0.39-15.71; rt-PA, 2.57, 0.74-5.00; rt-PA and hirulog, 1.95, 0.33-6.80; p = 0.32). Significant cerebral hemorrhage was observed in one placebo, two rt-PA, and three rt-PA plus hirulog treated animals. One fatal systemic hemorrhage was observed in each of the rt-PA groups. We conclude that rt-PA plus hirulog improves cerebral perfusion but does not necessarily reduce cerebral injury. DWI and PWI are useful methods for monitoring thrombolysis.

Animals↗
PubMed2006

Modeling low-coherence enhanced backscattering using Monte Carlo simulation.

Constructive interference between coherent waves traveling time-reversed paths in a random medium gives rise to the enhancement of light scattering observed in directions close to backscattering. This phenomenon is known as enhanced backscattering (EBS). According to diffusion theory, the angular width of an EBS cone is proportional to the ratio of the wavelength of light lambda to the transport mean-free-path length l(s)* of a random medium. In biological media a large l(s)* approximately 0.5-2 mm >> lambda results in an extremely small (approximately 0.001 degrees ) angular width of the EBS cone, making the experimental observation of such narrow peaks difficult. Recently, the feasibility of observing EBS under low spatial coherence illumination (spatial coherence length Lsc << l(s)*) was demonstrated. Low spatial coherence behaves as a spatial filter rejecting longer path lengths and thus resulting in an increase of more than 100 times in the angular width of low coherence EBS (LEBS) cones. However, a conventional diffusion approximation-based model of EBS has not been able to explain such a dramatic increase in LEBS width. We present a photon random walk model of LEBS by using Monte Carlo simulation to elucidate the mechanism accounting for the unprecedented broadening of the LEBS peaks. Typically, the exit angles of the scattered photons are not considered in modeling EBS in the diffusion regime. We show that small exit angles are highly sensitive to low-order scattering, which is crucial for accurate modeling of LEBS. Our results show that the predictions of the model are in excellent agreement with the experimental data.

Animals↗
PubMed2005

Perisylvian language networks of the human brain.

Early anatomically based models of language consisted of an arcuate tract connecting Broca's speech and Wernicke's comprehension centers; a lesion of the tract resulted in conduction aphasia. However, the heterogeneous clinical presentations of conduction aphasia suggest a greater complexity of perisylvian anatomical connections than allowed for in the classical anatomical model. This article re-explores perisylvian language connectivity using in vivo diffusion tensor magnetic resonance imaging tractography. Diffusion tensor magnetic resonance imaging data from 11 right-handed healthy male subjects were averaged, and the arcuate fasciculus of the left hemisphere reconstructed from this data using an interactive dissection technique. Beyond the classical arcuate pathway connecting Broca's and Wernicke's areas directly, we show a previously undescribed, indirect pathway passing through inferior parietal cortex. The indirect pathway runs parallel and lateral to the classical arcuate fasciculus and is composed of an anterior segment connecting Broca's territory with the inferior parietal lobe and a posterior segment connecting the inferior parietal lobe to Wernicke's territory. This model of two parallel pathways helps explain the diverse clinical presentations of conduction aphasia. The anatomical findings are also relevant to the evolution of language, provide a framework for Lichtheim's symptom-based neurological model of aphasia, and constrain, anatomically, contemporary connectionist accounts of language.

Adult↗
PubMedDate not supplied

[Modeling of swarm formation as a consequence of autotaxis].

The simple model of school and swarm formation is proposed within the frameworks of Eulerian space models (reaction-diffusion-advection system). Assuming that the schooling and the processes of birth-and-death act on different time scales, we have excluded the local kinetics of species (the reaction term) from the model. The spatial dynamics of animals is circumscribed by scalar field of density and vector field of velocity. The basis of animal aggregation in space is the ability of animals to move in certain direction, i.e. taxis. As an example of swarming strategy the behavior of midges is taken: we presume that individuals accelerate towards higher swarm density but change direction when the density exceeded some maximum. In other words, acceleration of movement is assumed to be proportional (with density-dependent coefficient of proportionality) to the gradient of species density. This statement poses the equation for species velocity. Thus, our model adds the differential equation for velocity of autotaxis to the standard advection-diffusion model. The linear analysis of 1D problem with zero-flux boundary conditions has showed that homogeneous nonzero equilibrium looses its stability when the movement rate of animals (coefficient of proportionality in velocity equation) overpasses some bifurcation value. The numerical experiments have confirmed analytical results, displaying stationary spatially heterogeneous solution (standing waves) for the detected supercritical value of the movement rate.

Animals↗
PubMed1999

[Intratumoral chemotherapy in an experimental animal model: another therapeutic possibility in cancerology].

OBJECTIVE: Assess the efficacy of intratumoral chemotherapy in a colonic tumor model implanted subcutaneously in the BD IX rat. METHOD: In order to determine their antitumoral effect, 5 anticancer drugs were administered via intravenous and direct intratumoral routes 2 or 10 days after subcutaneous inoculation of tumoral cells. Intratumoral diffusion was evaluated using Patent blue injected directly into the tumoral tissue. Cisplatinum was administered via intratumoral, intravenous and intra-arterial routes to determine the intratumoral and intrarenal concentrations achieved with each of these administration routes. Cisplatinum was also administered via intravenous and intratumoral infusion for 30 minutes to determine the antitumoral effect of each of these routes. RESULTS: Mitomycin and cisplatinum inhibited growth of tumors which had not yet become established and caused advanced stage tumors to regress. For early stage tumors, the intratumoral route was always more effective than the intravenous route. Patent blue diffusion demonstrated a nonhomogeneous intratumoral distribution. Compared with intravenous or intra-arterial infusion, intratumoral infusion gave much higher concentrations of cisplatinum within the tumors and reduced systemic diffusion. At 7 weeks, the antitumoral effect was equivalent for the 2 administration routes while at 13 weeks, the intratumoral treatment was more effective than the intravenous treatment. CONCLUSION: These findings in an experimental animal model demonstrate that intratumoral chemotherapy is more effective than intravenous chemotherapy. It is however still impossible to consistently cure tumors induced in animals.

Amiodarone↗
PubMed1999

Functional heterogeneity of oxygen supply-consumption ratio in the heart.

In this review, the regional heterogeneity of the oxygen supply-consumption ratio within the heart is discussed. This is an important functional parameter because it determines whether regions within the heart are normoxic or dysoxic. Although the heterogeneity of the supply side of oxygen has been primarily described by flow heterogeneity, the diffusional component of oxygen supply should not be ignored, especially at high resolution (tissue regions << 1 g). Such oxygen diffusion does not seem to take place from arterioles or venules within the heart, but seems to occur between capillaries, in contrast to data recently obtained from other tissues. Oxygen diffusion may even become the primary determinant of oxygen supply during obstructed flow conditions. Studies aimed at modelling regional blood flow and oxygen consumption have demonstrated marked regional heterogeneity of oxygen consumption matched by flow heterogeneity Direct, non-invasive indicators of the balance between oxygen supply and consumption include NADH videofluorimetry (mitochondrial energy state) and microvascular PO2 measurement by the Pd-porphyrin phosphorescence technique. These indicators have shown a relatively homogeneous distribution during physiological conditions supporting the notion of regional matching of oxygen supply with oxygen consumption. NADH videofluorimetry, however, has demonstrated large increases in functional heterogeneity of this ratio in compromised hearts (ischemia, hypoxia, hypertrophy and endotoxemia) with specific areas, referred to as microcirculatory weak units, predisposed to showing the first signs of dysoxia. It has been suggested that these weak units show the largest relative reduction in flow (independent of absolute flow levels) during compromising conditions, with dysoxia initially developing at the venous end of the capillary.

Animals↗
PubMed1990

Interactions between cell populations influence expression of the transformed phenotype in irradiated rat tracheal epithelial cells.

A combined in vivo-in vitro model has been utilized to evaluate the influence of cell-cell interactions on expression of radiation-induced transformation in irradiated rat tracheal epithelial cells. Two types of cell interactions are evaluated. One type of interaction appears to involve direct cell-cell contact as occurs within the intact tissue. The other type of communication appears to be mediated via a diffusible factor, most likely transforming growth factor type-beta. The data suggest the need to be cautious when extrapolating from transformation data obtained following irradiation of low-density rapidly proliferating cell cultures to the in vivo model.

Animals↗
PubMed2001

Vertebrate floor plate transiently expresses a compound recognized by antisera raised against subcommissural organ secretion.

Located along the ventral midline of the neural tube, the floor plate (FP) performs an essential role in central nervous system development, especially in the patterning of the ventral region of the neural tube and axonal guidance. Several studies have been directed to the identification of molecules mediating some of the functions of the FP. Most of the models proposed for floor plate actions involve contact-mediated- and/or gradients of diffusible-signals acting throughout the nervous tissue. This report presents and discusses findings showing that the FP cells secrete a novel compound, which is recognized by antisera raised against secretory products of the subcommissural organ (SCO). This immunoreactive compound appears to be very similar to one of the glycoproteins secreted by the SCO. This immunoreactivity is expressed transiently during central nervous system development, and its rostro-caudal extension along the anterior-posterior axis of the FP displays some species variations. However, a constant feature in all species investigated is that this immunoreactive compound is highly expressed in the FP located in the mesencephalic-metencephalic boundary. The distribution of this compound is compatible with basal and apical pathways of release from FP cells. The former might participate in the formation of some brain commissures. The latter might involve the use of the cerebrospinal fluid as a route for performing actions on distant targets, a pathway somehow disregarded by most models accounting for morphogen actions.

Animals↗
PubMed2005

Inference of multiple fiber orientations in high angular resolution diffusion imaging.

A method is presented that is capable of determining more than one fiber orientation within a single voxel in high angular resolution diffusion imaging (HARDI) data sets. This method is an extension of the Markov chain method recently introduced to diffusion tensor imaging (DTI) analysis, allowing the probability density function of up to 2 intra-voxel fiber orientations to be inferred. The multiple fiber architecture within a voxel is then assessed by calculating the relative probabilities of a 1 and 2 fiber model. It is demonstrated that for realistic signal to noise ratios, it is possible to accurately characterize the directions of 2 intersecting fibers using a 2 fiber model. The shortcomings of under-fitting a 2 fiber model, or over-fitting a 1 fiber model, are explored. This new algorithm enhances the tools available for fiber tracking.

Algorithms↗