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At least 379 records · Page 21Linked to original sources
PubMed1990

A mathematical model of atrioventricular conduction block using the excitability recovery curve of the myocardial cell.

A simple mathematical model of AV conduction block was constructed on the basis of single-cell electrophysiological experiments concerning the rate-dependent property of excitability of the AV nodal cells (the excitability recovery curve, ERC). This ERC was analogous to the phase response curve (PRC) of cardiac pacemaker cells, which the authors had previously used to construct a model of modulated parasystole. Computer simulation was used to reproduce the ERC. The single-cell ERC was then extended to the entire AV node, and this curve was used to formulate a mathematical model of AV conduction block as a nonlinear, first-order difference equation of the successive PR intervals of the ECG. This model predicted a variety of ECG patterns of AV conduction block: normal rhythm, first-degree block, and several second-degree blocks of complex Wenckebach periodicity in relation to the sinus rate and the shape of the ERC. By assuming this model it was possible to identify the underlying ERC of actual ECGs with complex Wenckebach periodicity.

Animals↗
PubMed1990

Modeling of cardiac rhythms. A signal-processing perspective.

The authors describe their perspective on the modeling of cardiac rhythms as a component of cardiac arrhythmia signal-processing algorithms. They emphasize that these models are for a specific end purpose and that the aspects of cardiac behavior that are captured by the models are only those relevant for the development of the signal-processing algorithms. The approach is to use statistics to describe ranges of cardiac behavior that share some common feature with respect to the purpose of the signal processing. The statistical approach has the advantage that, coupled with a statistical performance criterion, it specifies an optimal signal-processing algorithm. These optimal algorithms are often computationally intractable, however, especially for real-time use in instruments. Approximations are therefore crucial. The mathematical form of the model is then important since, even if two forms generate identical statistics, the approximations that are natural in different forms can be quite different. Two different mathematical formulations are described--stochastic Petri nets and interacting Markov chains--and the different types of approximately optimal signal-processing algorithms that are natural in these two frameworks are discussed.

Algorithms↗
PubMed1990

Simulation and experimental studies of the factors influencing the frequency spectrum of cardiac extracellular waveforms.

Spectral analysis of electrocardiographic signals has been proposed as a tool to detect features reflecting cardiac diseases, such as ventricular hypertrophy, myocardial infarction, and a predisposition to sustained ventricular tachycardia. The lack of a theoretical basis to address this question prompted the authors to undertake a simulation study using a bidomain volume conductor model of a strip of cardiac tissue, combined with Fourier analysis, and electrograms recorded from an isolated right atrial canine preparation. In the crista terminalis, the bandwidth of the normal electrogram was 840 +/- 200 Hz (mean +/- SD) during longitudinal propagation and 660 +/- 370 Hz during transverse propagation. During premature stimulation, signal bandwidth and propagation velocity increase with the coupling interval. In the model, a linear combination of Vmax and propagation velocity values allows simulation of the various features of premature excitation. Vmax is the major determinant of the high-frequency content of the signal. An important decrease in the high-frequency content of electrograms occurs when the recording electrode is moved away from the preparation or the simulation model; at distances larger than 1-5 mm, the bandwidth levels off to a value of 50-120 Hz. Partial blockade of axial current flow in the direction of propagation due to microscopic discontinuities and variable activation delays at these discontinuities may be the cause of fragmented activity in necrotic myocardium, which is associated with a reduced bandwidth. Thus, short- and long-term effects of ischemia followed by infarction, such as decreased propagation velocity, decreased action potential upstroke, and fragmentation, tend to decrease the electrocardiographic bandwidth.

Action Potentials↗
PubMed1990

Computer simulation of supraventricular tachycardia with the Wolff-Parkinson-White syndrome using three-dimensional heart models.

Supraventricular tachycardias with the Wolff-Parkinson-White (WPW) syndrome have been successfully simulated using a newly developed simulation system. The heart model, including atria and ventricles, was constructed of about 50,000 discrete elements (model cells) in three dimensions with 1.5-mm spatial resolution. The model cells covered all of the types of cells in the actual heart, including the normal myocardium, special conduction system and abnormal cells, such as the bundle of Kent (accessory pathway) and ectopic pacemaker (premature beat). Different model cells were specified by their electrophysiologic parameters, such as action potential, refractory period, and conduction velocity. The WPW syndrome was simulated by setting an accessory pathway between the right atrium and ventricle. Based on this model a premature atrial beat was introduced, which initialized the tachycardia. By adjusting the parameters, three types of reciprocal supraventricular tachycardia were simulated with the reentry circuits (1) formed anterogradely by the A-V node and retrogradely by the accessory pathway, (2) formed anterogradely by the accessory pathway and retrogradely by the A-V node, and (3) confined within the A-V node. Time relations for initializing and maintaining the tachycardias were evaluated. The simulated ECGs were in good agreement with the clinical findings.

Computer Simulation↗
PubMed1983

Difference equation model of ventricular parasystole as an interaction between cardiac pacemakers based on the phase response curve.

A model of extended ventricular parasystole proposed by Moe et al. (1977) was formulated as a system of nonlinear difference equations by using the phase response curve of myocardial pacemakers. A number of ECG patterns of ventricular arrhythmia such as bigeminy, trigeminy etc. were explained from the property of periodic solutions of the equation. Characteristic properties of special kinds of arrhythmia called "concealed bigeminy" and "concealed trigeminy" were derived mathematically by assuming the model, in relation to the equation of the analog neuron model. The present study was considered to be of clinical significance as a theoretical foundation for the study of genesis of cardiac arrhythmias.

Arrhythmias, Cardiac↗
PubMed1993

Spreading of excitation in 3-D models of the anisotropic cardiac tissue. I. Validation of the eikonal model.

In this work we investigate, by means of numerical simulations, the performance of two mathematical models describing the spread of excitation in a three dimensional block representing anisotropic cardiac tissue. The first model is characterized by a reaction-diffusion system in the transmembrane and extracellular potentials v and u. The second model is derived from the first by means of a perturbation technique. It is characterized by an eikonal equation, nonlinear and elliptic in the activation time psi(x). The level surfaces psi(x) = t represent the wave-front positions. The numerical procedures based on the two models were applied to test functions and to excitation processes elicited by local stimulations in a relatively small block. The results are in excellent agreement, and for the same problem the computation time required by the eikonal equation is a small fraction of that needed for the reaction-diffusion system. Thus we have strong evidence that the eikonal equation provides a reliable and numerically efficient model of the excitation process. Moreover, numerical simulations have been performed to validate an approximate model for the extracellular potential based on knowledge of the excitation sequence. The features of the extracellular potential distribution affected by the anisotropic conductivity of the medium were investigated.

Animals↗
PubMed1989

Red cell distribution at microvascular bifurcations.

The distribution of red cell and blood volume flow was studied at 65 arteriolar bifurcations in the rat mesentery. Hematocrit and flow velocity were measured simultaneously in all three vessel segments constituting a bifurcation. Blood flow distribution was manipulated by irreversibly occluding downstream side branches of one of the daughter vessels. The dependence of fractional red cell volume flow on fractional blood flow was described using a three-parameter (X0, B, A) logit function. The critical volume flow fraction below which only plasma enters a downstream branch (X0), the nonlinearity of the relation between red cell and blood volume flow (B), and the asymmetry of that relation which is described by the parameter A decrease with increasing diameter of the vessel feeding the bifurcation. At diameters above 30 microns, phase separation is very limited. In addition, the nonlinearity parameter B decreases with decreasing hematocrit in the feeding vessel. The asymmetry parameter A strongly depends on the diameter ratio between the two daughter branches: For a given fractional blood flow, the smaller branch receives more red cells than the larger branch. Using a model for plasma skimming based on the assumption of a planar separating surface, the shape of the radial hematocrit profile in the feeding vessel has been calculated. The model predicts a decrease in local hematocrit from the vessel axis toward the wall with a distinct marginal zone free from cell centers. With increasing vessel diameter the hematocrit profile becomes more blunted while the width of the marginal zone increases.

Animals↗
PubMed1989

Flow behavior of neonatal and adult erythrocytes in narrow capillaries.

This study was designed to analyze the flow behavior of red blood cells (RBCs) in circular vessels with diameters of 3 to 6 microns by means of a mathematical model. According to this model, the RBC flow velocity is 1 mm/sec, RBCs assume axisymmetric shape, and the gap between the RBC and the vessel wall allows sufficient lubrication. The flow resistance depends on the surface area and volume of RBCs, the plasma viscosity, and the vessel diameter. Surface area and volume of RBCs from 10 term neonates and 10 adults were determined by means of a micropipet system and plasma viscosity was measured using a capillary viscometer. Neonatal RBCs had larger volumes (107 +/- 6 fl vs 90 +/- 4 fl) and surface areas (154 +/- 7 microns 2 vs 137 +/- 7 microns 2) than adult RBCs (P less than 0.005). Plasma viscosity was lower in neonates than in adults (1.04 +/- 0.10 cP vs 1.26 +/- 0.13 cP; P less than 0.005). The flow model leads to the following conclusions: During the passage of 3- to 6- microns vessels, the large neonatal RBCs are more elongated than the smaller adult RBCs. In vessels with diameters of less than 3.3 microns, the rear of neonatal RBCs becomes convex, whereas this critical vessel diameter is 3.1 microns for adult RBCs. If the cells are suspended in the same medium, neonatal RBCs require a 31% higher driving pressure than adult RBCs to achieve the necessary elongation for passing through a narrow capillary. However, both cell types require similar driving pressures, if the cells are suspended in the corresponding plasma. The tube/discharge hematocrit ratio of neonatal RBCs is 1 to 6% higher than that of adult cells. Relative viscosity of neonatal RBCs is approximately 7% higher compared with adult RBCs, whereas the blood viscosity (relative viscosity times plasma viscosity) is 12% less in neonates than in adults. We conclude that the large size of neonatal RBCs may cause impaired flow in narrow vessels with diameters below the critical value of 3.3 microns. In vessels with diameters of 3.3-6.0 microns, the disadvantage of the large size of neonatal RBCs appears to be completely compensated for by the lowr plasma viscosity in the neonate.

Adult↗
PubMed1987

Theoretical evaluation of energy loss methods in the analysis of prosthetic heart valves.

The purpose of this paper is to clarify certain aspects of the 'energy loss' approach to the analysis of artificial heart valves. This involves the discussion of what is meant by 'energy loss'; the derivation of an appropriate energy equation; the scrutiny of the conditions under which it may be applied and of the assumptions involved in deriving a useful formulation in terms of readily measurable parameters; consideration of the extent to which these assumptions are valid in reported experiments using this formulation and the demonstration of the suitability and versatility of this approach when applied specifically to heart valve conduits.

Biomedical Engineering↗
PubMed1987

Model of the haemodynamic reactions to intermittent coronary sinus occlusion.

Coronary sinus pressure data have been obtained from anaesthetized dogs during pressure controlled intermittent coronary sinus occlusion. It is the main aim of this paper to provide a mathematical procedure for modelling the typical time course of sinus pressure after temporary obstruction of the sinus. The model is produced by fitting a parameterized function to the systolic and diastolic pressures in order to represent mathematically the shape of the curves. The parameters characterize the rise in coronary sinus pressure following occlusion, and are used to calculate 'derived quantities' which mimic the physician's visual assessment of trace recordings and their clinical implications in certain forms of coronary sinus pressure reaction. This procedure should be thought of as a kind of pattern recognition which reflects the changing state of the myocardium. The mathematical results are shown to bear a close resemblance to the clinical effects of coronary sinus occlusion.

Animals↗
PubMed1991

Accuracy of colour Doppler ultrasound velocity measurements in small vessels.

Colour Doppler ultrasound offers the possibility of imaging small vessels not visible by B-mode alone. The colour Doppler image of velocities allows the course of small vessels to be imaged in the X-Y plane of the scan provided the Doppler frequency shift is of sufficient magnitude. This permits alignments of the Doppler cursor, allowing angle correction to provide true velocity measurements from the Doppler shift obtained. Before attempting to make velocity measurements, however, it is essential to be aware of the possible error in the Z plane caused by the thickness of the Doppler sample volume. To quantify this source of error, hydrophone and flow-rig measurements were performed on an Acuson 128 colour Doppler scanner with both 5 MHz linear-array and 3.5 MHz phased-array transducers. Measurements of the transmitted pulses using a point hydrophone showed that both probes employ approximately 3.5 MHz Doppler pulses (in both colour and pulsed Doppler modes). The two transducers have the same axial resolution. In colour Doppler mode the axial length of the sample volume increases automatically with depth by up to 0.5 mm. Measurements of colour and pulsed Doppler signal strength were obtained in a controlled flow rig. Both transducers produced accurate colour flow images of the phantom at their optimum depths; flow velocity errors due to Z-plane thickness are less than 5%. There was, however, substantial error outside these optimum conditions (up to 20%).

Arteries↗
PubMed1992

Computer simulation of the effects of ventricular interdependence on indices of left ventricular systolic function.

The influence of ventricular interdependence on cardiovascular function has been convincingly demonstrated. In the intact cardiovascular system ventricular interdependence is always present, and thus measures of cardiac function include the contribution of ventricular interdependence (VI). A cardiovascular system model is presented and used to discuss how VI affects selected indices of left ventricular (LV) systolic function. Indices of LV function studied were the ejection fraction, stroke work, peak time derivative of ventricular pressure (dP/dT) and the LV end-systolic pressure-volume relationship. The effects of right ventricular (RV) volume through systolic VI on these indices are conveniently studied by comparing the model responses to pulmonary artery (PA) and vena caval (VC) occlusions; both PA and VC occlusion reduce LV volume, but the RV volume is increased by PA but reduced by VC occlusions. Through systolic VI the increase in RV volume with PA occlusion shifted the LV end-systolic pressure-volume relationship to the left and thus affected measures of LV maximum elastance. The LV ejection fraction, peak dP/dT and stroke work were all augmented by the increase in RV volume associated with the PA occlusion. Experimental studies comparing the responses to PA and VC occlusions are in broad agreement with the results described here. Systolic VI also shifted the cardiac function curve, a global measure of cardiac function, to the left. The results thus suggest that commonly used indices of LV systolic function are dependent on RV function and do not solely reflect LV function.

Cardiac Volume↗
PubMed1993

Volume profiles obtained by a conductimetric method.

One problem faced by intracardiac conductance volumetry is the non-uniform distribution of the injected current. Salo, in 1989, proposed a method to correct this undesirable effect. The objective here is to test Salo's method in known volumes of simple geometry by obtaining volume profiles. A plastic rod with 15 metallic rings simulated the conductance catheter. Five sections were used for the resistance measurements employing the upper electrode as fixed current source and the lowest one as the shifting source. This is part of Salo's procedure. The source-to-section distance was measured from the moving source to the section (linear definition) or using the equivalent distance concept (Salo's). Thereafter, each sectional resistance set of values was plotted as a function of the inverse of the source-to-section distance (either definition) elevated to an empirical exponent k to obtain the corrected sectional resistance by extrapolation back to zero of the regression line, i.e., a value produced by a source theoretically placed at infinity. In addition, a mathematical analysis was attempted, searching for an optimum k based on minimum volume error. The best volume profiles for two cylinders and a frustum were obtained with k = 2 using the linear definition of distance (errors of -3.49%, -1.25% and -3.65%, respectively). Moreover, the frustum angle was determined within 0.4 degrees (2.7%) of the real value. The theoretical analysis led to an inverse logarithmic relationship between the exponent k and the source-to-section distance.(ABSTRACT TRUNCATED AT 250 WORDS)

Cardiac Volume↗
PubMed1993

Flow studies on atriopulmonary and cavopulmonary connections of the Fontan operations for congenital heart defects.

A comparative flow study has been conducted on two configurations of the Fontan operations for congenital heart defects in which the right ventricle is by-passed. The study was made on rigid in vitro models of the atriopulmonary and cavopulmonary connections under steady-flow conditions. It involved using pressure and flow measurements to determine the pressure-drop coefficient, pressure-energy-loss coefficient and total-energy-loss coefficient. The cavopulmonary model was found to have much lower flow losses compared to the atriopulmonary model, especially at flow rates about 5 l min-1.

Anastomosis, Surgical↗
PubMed1992

Increased cardiac production of dihydroxyphenylalanine (DOPA) during sympathetic stimulation in anaesthetized dogs.

Entry of dihydroxyphenylalanine (DOPA) into plasma from specific organs may reflect regional activity of tyrosine hydroxylase, the enzyme responsible for the immediate synthesis of DOPA and rate-limiting for subsequent formation of catecholamines. Therefore, cardiac spillovers of DOPA, noradrenaline and the intraneuronal metabolite of noradrenaline, dihydroxyphenylglycol (DHPG), were examined during two periods of graded electrical stimulation of the sympathetic nerves to the heart in anesthetized dogs. Responses were examined before and after neuronal uptake blockade with desipramine. Cardiac spillover of DOPA increased by 1.8- and 4.4-fold during sympathetic stimulation before desipramine and by 1.6- and 3.3-fold after desipramine. Fold increases in cardiac spillover of DOPA were much lower than but positively related with fold increases in noradrenaline spillover (5.9- and 13.8-fold increases before and 9.0- and 15.8-fold increases after desipramine). Increases in cardiac spillover of DHPG (1.5- and 2.3-fold increases) were blocked by desipramine so that fold changes in spillover of DOPA were greater than and poorly related to changes in spillover of DHPG. Fold increases in cardiac spillover of DOPA showed a close one-to-one positive relationship with fold increases in the sum of cardiac spillovers of noradrenaline and dihydroxyphenylglycol before and after desipramine. For a given fold increase in noradrenaline release, transmitter turnover is increased fractionally and noradrenaline synthesis need also only increase fractionally to maintain transmitter stores constant. The close relationship between fold increases in cardiac spillover of DOPA and combined spillovers of noradrenaline and DHPG is consistent with regulation of tyrosine hydroxylase activity to match changes in noradrenaline synthesis with changes in noradrenaline turnover. Changes in cardiac spillover of DOPA appear to reflect local changes in tyrosine hydroxylase activity.

Animals↗
PubMedDate not supplied

Hemodynamics of the normal human carotid bifurcation: in vitro and in vivo studies.

The spatial and temporal characteristics of blood flow in the normal adult human carotid bifurcation are investigated by two different methods: in vitro pulsatile flow model experiments using laser Doppler anemometry and in vivo studies employing pulsed Doppler velocity measurements obtained with an ultrasound duplex scanner. Glass and Plexiglas models based upon arteriographic measurements were evaluated with laser Doppler anemometer methods for pulsatile flow. A similarity approach permits the model study to be geometrically and hydrodynamically accurate with respect to the human carotid bifurcation. These parallel but separate approaches were originally performed by the principal authors without knowledge of each others' work. Normal flow patterns in the proximal internal carotid artery are demonstrated to include: unidirectional, helical, transient reversal, and low velocity regions of flows. The characterization of these complex temporal and spatially variant flow fields required the high sample volume resolution afforded by the model study. Pulsed Doppler ultrasound and a novel method of positioning the sample volume permitted a qualitative description of the complex flow velocity fields in the normal human bifurcation. Results of the two methods are compared and a striking similarity between the two methods is observed for the primary and secondary flow features. The problem of associating blood flow velocity disturbances with the presence of intralumenal disease is addressed in the discussion. It is suggested that the flow disturbances associated with the normal carotid bifurcation are different from those associated with intraluminal disease and further, that the secondary flow structures can be usefully employed to establish normalcy.

Adult↗