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At least 721 records · Page 40Linked to original sources
PubMed2003

Database deconvolution.

A new deconvolution technique is described. It regards the Rutland-Patlak plot as the integral of the retention function, and performs deconvolution by creating and then differentiating the Rutland-Patlak plot. The reasoning behind this approach is that in producing the Rutland-Patlak plot, both the content function and the integral of the input function are divided by the input function (i.e. the blood curve), and that this has the effect of producing data equivalent to that which would be produced if the input function did not vary (i.e. if there were a constant blood level of tracer). The concept was tested against data created by modelling techniques. It was able to reproduce retention functions with a variety of different shapes that were used to produce the artificial renogram data. The new deconvolution method is sufficiently simple to be used in either a database or a spreadsheet and does not require any special program units to be written. It does not appear to make any assumptions about the data nor the shape of the retention function, and does not appear to be vulnerable to the oscillating errors that sometimes occur in iterative deconvolution.

Algorithms↗
PubMed1994

New concepts in the study of tissue vascularization: a mathematical model of skin vascularization.

A preliminary study demonstrated the existence of a fractal structure for perforator arterial vessels of the skin and proved to be a useful tool to compare vascular trees on the basis of their complexity. Fractal analysis of axial-perforator arteriovenous vascular trees was performed on the skin of mice after injection of the arterial network by india ink. Fractal analysis was performed by box counting. Fractal dimension D was determined for 35 venous and 31 arterial perforator vessels (D = 1.302 and 1.264, respectively) and 5 venous and 3 arterial axial vessels (D = 1.374 and 1.328, respectively) (r2 > or = 0.985). All vascular networks show a fractal structure, characterized by a specific D. These values are relatively constant; D is a function of the anatomic and physiologic characteristics. There was no significant difference between venous and arterial networks, nor was there between axial and perforator networks (p < 0.05); this demonstrates a similar efficacy in terms of perfusion of the skin. A computer simulation based on fractal theory has been developed to reproduce the two kinds of vascular networks. Fractals are the result of a construction procedure that is repeated and repeated so that the iteration of a very simple rule can produce seemingly complex shapes, such as vascular networks. The basic module that is repeated in the whole structure is Y-shaped and is termed the generator; this generator is applied to a basic structure, called the initiator. After a few iterations, a vascular network is obtained. The difference between axial and perforator vascular networks is the choice of the initiator, whereas the generator is identical.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1999

Computer simulation of intracranial pressure changes during induction of anesthesia: comparison of thiopental, propofol, and etomidate.

We have developed a computer model of cerebrovascular hemodynamics that interacts with a pharmacokinetic drug model. We used this model to examine the effects of various stimuli occurring during anesthesia on cerebral blood flow (CBF) and intracranial pressure (ICP). The model is a seven-compartment constant-volume system. A series of resistances and compliances relate blood and cerebrovascular fluid fluxes to pressure gradients between compartments. Variable arterial-arteriolar resistance (Ra-ar) and arteriolar-capillary resistance (Rar-c) simulate autoregulation and drug effects, respectively. Rar-c is also used to account for the effect of CO2 on the cerebral circulation. A three-compartment pharmacokinetic model predicts concentration-time profiles of intravenous induction agents. The effect-site compartment is included to account for disequilibrium between drug plasma and biophase concentrations. The simulation program is written in VisSim dynamic simulation language for an IBM-compatible personal computer. Using the model, we have predicted ICP responses during induction of anesthesia for a simulated patient with normal as well as elevated ICP. Simulation shows that the induction dose of intravenous anesthetic reduces ICP up to 30% (propofol > thiopental > etomidate). The duration of this effect is limited to less than 5 minutes by rapid drug redistribution and cerebral autoregulation. Subsequent laryngoscopy causes acute intracranial hypertension, exceeding the initial ICP. ICP elevation is more pronounced in a nonautoregulated cerebral circulation. Simulation results are in good agreement with the available experimental data. The presented model allows comparison of various drug administration schedules to control ICP.

Anesthetics, Intravenous↗
PubMed2006

A local pre-receptor mechanism of hormone stimulus amplification: focus on angiotensin II in resistance blood vessels.

BACKGROUND: The in-vivo correlation between vascular tone and the concentration of free angiotensin (Ang) II at the level of the arterioles, under (patho)physiological conditions, is not known. OBJECTIVE: To examine the in-vivo kinetics of binding of Ang II to Ang II type 1 (AT1) receptors in vascular tissue. METHODS AND RESULTS: A plane vascular smooth muscle (VSM) sheet containing a single layer of cells, at one side exposed to Ang II, was the starting point for designing a mathematical model based on local receptor density and geometric considerations and on kinetic parameters of Ang II diffusion and Ang II-AT1 receptor complex formation and internalization. Calculations demonstrate that a diffusing Ang II molecule at short distance from the receptor has an almost 100% chance to be actually bound, so that the apparent binding rate constant (per unit of receptor concentration) is greatly augmented. This pre-receptor stimulus amplification (PRESTAMP) mechanism is sustained by AT1 receptor-mediated endocytosis and receptor recycling. On the other hand, PRESTAMP also enhances endocytotic receptor downregulation, and calculations predict that steady-state levels of Ang II above threshold have relatively little additional effect. CONCLUSION: The results explain why physiological concentrations of free Ang II far below the equilibrium dissociation constant of its reaction with AT1 receptors are sufficient to increase vascular resistance, and why a correlation between blood pressure and the concentration of free Ang II is often difficult to demonstrate.

Angiotensin II↗
PubMedDate not supplied

Intravascular blood oxygenation using hollow fibers in a disk-shaped configuration: experimental evaluation of the relationship between porosity and performance.

Implantation of hollow fibers for blood oxygenation within a human vessel has been investigated for the last 15 years. Unfortunately, the combination of limited space inside the venous system and disadvantageous blood flow conditions has resulted until now in limited gas exchange performance of the investigated oxygenators. We are developing a highly integrated intravascular membrane oxygenator (HIMOX) characterized by a homogeneous disk-shaped fiber configuration. The main advantages are a larger fiber surface as well as favorable cross flow through the fibers compared with earlier designs. Fiber porosity represents an important constructive parameter and leads to a trade-off when dimensioning the bundles with the aim of maximum gas exchange at small anatomical size. Low porosity results in higher fiber surface as well as blood velocity. Both effects potentially enhance the gas exchange, but the associated increase of the pressure drop leads to a deformation of the fiber bundle and to a blood shunt. This fluid-structure interaction influences the gas exchange in a complex way. We investigated the influence of porosity on the gas exchange in the proposed fiber configuration in vitro. Bundle deformation was proven by comparing experimental data with a theoretical model. Highest oxygen exchange supplied by a single bundle was achieved at an intermediate porosity of 0.575. Moreover, specific oxygen exchange per fiber surface, which is an indicator of favorable flow conditions, increased with increasing fiber porosity. We achieved up to 450 ml O2 min m, which is a promising result for intravascular membrane oxygenation.

Equipment Design↗
PubMed2003

A theoretical model of oxygen delivery and metabolism for physiologic interpretation of quantitative cerebral blood flow and metabolic rate of oxygen.

The coupling of cerebral blood flow (CBF) and metabolic rate of oxygen (CMRO2) during physiologic and pathophysiologic conditions remains the subject of debate. In the present study, we have developed a theoretical model for oxygen delivery and metabolism, which describes the diffusion of oxygen at the capillary-tissue interface and the nonlinear nature of hemoglobin (Hb) affinity to oxygen, allowing a variation in simple-capillary oxygen diffusibility, termed "effective oxygen diffusibility (EOD)." The model was used to simulate the relationship between CBF and CMRO2, as well as oxygen extraction fraction (OEF), when various pathophysiologic conditions were assumed involving functional activation, ischemia, hypoxia, anemia, or hypo- and hyper-capnic CBF variations. The simulations revealed that, to maintain CMRO2 constant, a variation in CBF and Hb required active change in EOD. In contrast, unless the EOD change took place, the brain allowed small but significant nonlinear change in CMRO2 directly dependent upon oxygen delivery. Application of the present model to quantitative neuroimaging of CBF and CMRO2 enables us to evaluate the biologic response at capillary level other than Hb- and flow-dependent properties of oxygen transport and may give us another insight regarding the physiologic control of oxygen delivery in the human brain.

Biological Transport↗
PubMed2006

Asymptotic properties of mathematical models of excitability.

We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (Hodgkin & Huxley 1952 J. Physiol.117, 500-544) model of nerve axon, Noble (Noble 1962 J. Physiol.160, 317-352) model of heart Purkinje fibres and Courtemanche et al. (Courtemanche et al. 1998 Am. J. Physiol.275, H301-H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al. kinetics.

Action Potentials↗
PubMed2006

The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue.

Electrical heterogeneities play a role in the initiation of cardiac arrhythmias. In certain pathological conditions such as ischaemia, current sinks can develop in the diseased cardiac tissue. In this study, we investigate the effects of changing the amount of heterogeneity and intercellular coupling on wavefront stability in a cardiac cell culture system and a mathematical model of excitable media. In both systems, we observe three types of behaviour: plane wave propagation without breakup, plane wave breakup into spiral waves and plane wave block. In the theoretical model, we observe a linear decrease in propagation velocity as the number of heterogeneities is increased, followed by a rapid, nonlinear decrease to zero. The linear decrease results from the heterogeneities acting independently on the wavefront. A general scaling argument that considers the degree of system heterogeneity and the properties of the excitable medium is used to derive a dimensionless parameter that describes the interaction of the wavefront with the heterogeneities.

Action Potentials↗
PubMed1997

Deviations from uniform power law scaling in nonstationary time series.

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.

Adult↗
PubMed2001

Coexistence of multiple spiral waves with independent frequencies in a heterogeneous excitable medium.

We studied the interactions and coexistence of stable spiral waves with independent frequencies in a heterogeneous excitable medium, using numerical simulations of a spatial system based on the FitzHugh-Nagumo cell model. When the heterogeneity of the medium exceeded a critical value, a transition took place from a single dominant spiral wave to a coexistence of multiple spiral waves with independent frequencies and n:n-1 wave conduction blocks. In this case, multiple spiral waves could coexist because they are "insulated" from each other by chaotic regions.

Biological Clocks↗
PubMed2003

Condition for alternans and stability of the 1:1 response pattern in a "memory" model of paced cardiac dynamics.

We analyze a mathematical model of paced cardiac muscle consisting of a map relating the duration of an action potential to the preceding diastolic interval as well as the preceding action potential duration, thereby containing some degree of "memory." The model displays rate-dependent restitution so that the dynamic and S1-S2 restitution curves are different, a manifestation of memory in the model. We derive a criterion for the stability of the 1:1 response pattern displayed by this model. It is found that the stability criterion depends on the slope of both the dynamic and S1-S2 restitution curves, and that the pattern can be stable even when the individual slopes are greater or less than one. We discuss the relation between the stability criterion and the slope of the constant-BCL restitution curve. The criterion can also be used to determine the bifurcation from the 1:1 response pattern to alternans. We demonstrate that the criterion can be evaluated readily in experiments using a simple pacing protocol, thus establishing a method for determining whether actual myocardium is accurately described by such a mapping model. We illustrate our results by considering a specific map recently derived from a three-current membrane model and find that the stability of the 1:1 pattern is accurately described by our criterion. In addition, a numerical experiment is performed using the three-current model to illustrate the application of the pacing protocol and the evaluation of the criterion.

Action Potentials↗
PubMed2003

Approximate analytical solutions of the Bidomain equations for electrical stimulation of cardiac tissue with curving fibers.

The mechanism by which an applied electric field stimulates cardiac tissue far from the stimulating electrodes is not wholly understood. One possible mechanism relates the curving cardiac fibers to the induced membrane currents and transmembrane potentials. However, we lack a qualitative understanding of where these areas of polarization will occur when an electric field is applied to a sheet of cardiac tissue with curving fibers. In our study, we derive an analytical model for the transmembrane potential, dependent on the gradient of the fiber angle theta, for a two-dimensional passive sheet of cardiac tissue exhibiting various fiber geometries. Unequal anisotropy ratios are crucial for our results. We compare the results from our analytical solution to a numerical calculation using the full bidomain model. The results of our comparison are qualitatively consistent, albeit numerically different. We believe that our analytical approximation provides a reliable prediction of the polarization associated with an electric field applied to cardiac tissue with any fiber geometry and a qualitative understanding of the mechanisms behind the virtual electrode polarization.

Animals↗
PubMed2003

Characterization of flow reduction properties in an aneurysm due to a stent.

We consider a lattice Boltzmann simulation of blood flow in a vessel deformed by the presence of an aneurysm. Modern clinical treatments involve introducing a stent (a tubular mesh of wires) into the cerebral artery in order to reduce the flow inside the aneurysm and favor its spontaneous reabsorption. A crucial question is to design the stent with suitable porosity so as to produce the most effective flow reduction. We propose a stent positioning factor as a characterizing tool for stent pore design in order to describe the flow reduction effect and reveal the several flow reduction mechanisms using this effect.

Aneurysm, Ruptured↗
PubMed2003

Stability and bifurcation in an integral-delay model of cardiac reentry including spatial coupling in repolarization.

We present the bifurcation analysis of a revised version of the integral-delay model [Courtemanche et al., Siam J. Appl. Math. 56, 119 (1996)] of reentry in a one-dimensional ring that includes a spatial coupling in the calculation of the action potential duration. This coupling is meant to reproduce the modulation of repolarization by the diffusive current flowing through the intercellular resistance. We show that coupling modifies the criterion for the stability of the period-1 solution, which is no longer uniquely related to the action potential restitution curve, but depends also on the degree of coupling between cells and on the dispersion relation of the velocity. Coupling also changes the scenario from an infinite-dimension Hopf bifurcation to a finite sequence of Hopf bifurcations that take place at different ring lengths.

Action Potentials↗
PubMed2003

Influence of nonexcitable cells on spiral breakup in two-dimensional and three-dimensional excitable media.

We study spiral wave dynamics in the presence of nonexcitable cells in two-dimensional (2D) and three-dimensional (3D) excitable media, described by the Aliev-Panfilov model. We find that increasing the percentage of randomly distributed nonexcitable cells can prevent the breaking up of a spiral wave into a complex spatiotemporal pattern. We show that this effect is more pronounced in 2D than 3D excitable media. We explain the observed 2D vs 3D differences by a different dependence of the period and diastolic interval of the spiral wave on the percentage of nonexcitable cells in 2D and 3D excitable media.

Animals↗
PubMed2004

Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics.

We investigate a two-dimensional mapping model of a paced, isolated cardiac cell that relates the duration of the action potential to the two preceding diastolic intervals as well as the preceding action potential duration. The model displays rate-dependent restitution and hence memory. We derive a criterion for the stability of the 1:1 response pattern displayed by the model. This criterion can be written in terms of experimentally measured quantities-the slopes of restitution curves obtained via different pacing protocols. In addition, we analyze the two-dimensional mapping model in the presence of closed-loop feedback control. The control is initiated by making small adjustments to the pacing interval in order to suppress alternans and stabilize the 1:1 pattern. We find that the domain of control does not depend on the functional form of the map, and, in the general case, is characterized by a combination of the slopes. We show that the gain gamma necessary to establish control may vary significantly depending on the value of the slope of the so-called standard restitution curve (herein denoted as S12), but that the product gammaS12 stays approximately in the same range.

Action Potentials↗
PubMed2004

Stochastic heart-rate model can reveal pathologic cardiac dynamics.

A simple one-dimensional Langevin-type stochastic difference equation can simulate the heart-rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical of Gaussian noise, and both parts can be directly determined from measured heart-rate data. Data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points. Studies of 15 congestive heart-failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points. Direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects. Results directly indicate that pathologic situations simplify the heart-rate control system.

Computer Simulation↗