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PubMed1992

Color Doppler determination of regurgitant flow: from proximal isovelocity surface areas to proximal velocity profiles. An in vitro study.

There is not yet a completely satisfactory Doppler method for determining the severity of valvular regurgitation. Recently, interest has focused on the so-called "flow convergence region." Color Doppler provides a longitudinal velocity profile of the flow convergence region proximal to restrictive orifices. With respect to determination of regurgitant flow rate, we studied the influence of orifice flow rate and orifice size on the proximal velocity profile. In a phantom model, flow across circular orifices was studied. The distance r (v) of discrete velocities detected proximal to the orifice was measured along the flow center line. Velocity profiles were established. (1) Proximal isovelocity surfaces: The radius r (v) also represented the central radius of the proximal isovelocity surfaces. Increases in flow resulted in larger central radii r (v). Application of the continuity equation and analysis of the resulting values yielded a radius and an orifice size dependence of the geometric isovelocity surface shape. Therefore, their surface area and flow rate could not be calculated from these axial measurements alone. (2) Proximal velocity profiles: The resulting hyperbolic velocity profile curves (x axis = velocity [v], y axis = distance [r (v)]) are shifted rightward by increases in flow. In contrast, increases in orifice size make the curve steeper, but large r (v) are not affected. This differential influence of flow rate and orifice size allows orifice size independent determination of flow rate. A nomogram is presented as one possible method for flow determination.

Blood Circulation↗
PubMed1992

Regurgitant volume estimation in patients with mitral regurgitation: initial studies using color Doppler "proximal isovelocity surface area" method.

Doppler color flow mapping of a proximal isovelocity surface area (PISA), calculated from a blue-red aliasing radius, has been shown in vitro to be accurate for estimating volume flow rate across a narrowed orifice. Volume flow rate (in cm 3/sec) can be calculated as PISA (in cm 2) x aliasing velocity (in cm/sec). This method has advantages over other color Doppler approaches in that PISA-derived volume flow rate calculations appear to be independent of machine parameter settings and orifice shape. We evaluated the clinical applicability of the PISA method in 49 patients with native valve mitral regurgitation (MR). Color Doppler flow mapping was performed at color aliasing velocities of 54-72 cm/sec. Twenty-four patients were excluded because a color aliasing radius was not clearly seen: 20 of these 24 patients had mild MR. In the remaining 25 patients, the ratio of maximum regurgitant jet area-to-left atrial area, as well as the regurgitant stroke volume estimated using the time-velocity integral method, were compared to regurgitant stroke volume calculated from the PISA method. Maximum PISA was calculated using a formula derived from previous in vitro studies: PISA = 8.05 x r 2, where r is the maximum color Doppler aliasing radius in the apical four-chamber view.(ABSTRACT TRUNCATED AT 250 WORDS)

Blood Flow Velocity↗
PubMed2000

Influence of the orifice inlet angle on the velocity profile across a flow convergence region by color Doppler in vitro.

The converging flow field proximal to a leaking valve is determined among other things by the orifice inlet angle formed by the leaflets. Thus, the inlet angle affects the determination of regurgitant flow rate by the flow convergence method. Based on the hypothesis of spheric isovelocity surfaces, others had postulated that a local velocity within the flow convergence should change inversely proportional to changes in the three-dimensional inlet angle. This concept would allow correction of the determination of regurgitant flow for nonplanar orifice inlet angles. We tested this concept in vitro. In a flow model, the flow convergence region proximal to different orifice plates was imaged by color Doppler: funnel-shaped, planar and tip-shaped (inverted funnels) orifice plates, with circular orifices of 2- and 7-mm diameter. Velocity profiles across the flow convergence along the flow centerline were read from the color maps. As predicted, the local velocities were inversely related to the inlet angle, but only at the 2-mm funnel orifices, this effect was inversely proportional to the three-dimensional inlet angle (i.e., in agreement with the mentioned concept). However, for any 7-mm orifice and/or inlet angle of > 180 degrees, the effect of the inlet angle was considerably less than predicted by the aforementioned concept. With increasing orifice diameter and with decreasing distance to the orifice, the effect of the orifice inlet angle was reduced. The effect of the orifice inlet angle on the flow convergence region is modulated by orifice size and the distance to the orifice. Therefore, correction of flow estimates in proportion to the three-dimensional inlet angle will lead to considerable errors in most situations of clinical relevance, namely to massive overcorrection when analyzing velocities located close to wide orifices.

Blood Flow Velocity↗
PubMed2006

A segmental polynomial model of ventricular electrograms as a simple and efficient morphology discriminator for implantable devices.

BACKGROUND: The goal of this study is to construct a polynomial model of the ventricular electrogram (EGM) that faithfully reproduces the EGM and can be implemented in current, low computational power implantable devices. Such a model of ventricular EGMs is still lacking. METHODS: New Zealand White rabbits underwent chronic implantation of pacemakers through a left thoracotomy approach. Unipolar ventricular EGMs sampled at a frequency of 1 kHz were stored digitally in 1-minute segments before and after intravenous injection of isoproterenol or procainamide. Each cardiac cycle was divided into a QR and an RQ segment which were modeled separately using a 6th order polynomial equation. RESULTS: The 14 coefficients of each cardiac cycle were reproducible throughout the baseline recordings (r > or = 0.94, P < 0.002). Isoproterenol caused no changes in the coefficients of the QR segment but significantly altered all but one of the seven coefficients of the RQ segment (p(6)= 0.0039, p(5)= 0.017, p(4)= 0.00007, p(3)= 0.112, p(2)= 0.00016, p(1)= 0.0086, p(a)= 0.00003). Procainamide caused statistically significant changes in both QR segment (p(6)= 0.018, p(5)= 0.287, p(4)= 0.019, p(3)= 0.176, p(2)= 0.016, p(1)= 0.362, p(a)= 0.000044) and RQ segment (p(6)= 0.0028, p(5)= 0.036, p(4)= 0.002, p(3)= 0.058, p(2)= 0.022, p(1)= 0.718, p(a)= 0.0018) coefficients. CONCLUSION: Our data demonstrate the feasibility of a segmental polynomial equation that reproduces the phases of depolarization and repolarization of the rabbit EGM. This model is reproducible and demonstrates the expected changes with antiarrhythmic drug administration. If reproduced in humans, these findings can have wide applications in patients with implantable devices, ranging from morphologic discrimination of arrhythmias to early detection of metabolic derangements or drug effects.

Animals↗
PubMed1988

Structural and functional variations in capillary systems within the brain.

The major hypothesis of this study is that there are differences among brain areas in capillary bed structure and function. Three general differences between circumventricular organ and non-CVO capillary beds were found. First, the PS products for AIB were about 300 times greater in CVO capillaries than in non-CVO (blood-brain barrier) capillaries. Second, the frequency of endothelial cell fenestrations was much greater in CVO capillaries than in non-CVO capillaries and the fenestrae may be structural modifications of endothelial cells that permit ready passage of solutes such as AIB. Third, the frequency of mitochondria was greater in BBB capillaries than in CVO capillaries; this high metabolic potential of BBB capillaries may be associated, in part, with "carrier-mediated" transport of various solutes between plasma and cerebral interstitial fluid. Capillary bed differences among all (i.e., both CVO and non-CVO) brain structures were also observed. Among these differences are: rate of blood flow, mean transit time of albumin, capillary volume and surface area, perfused microvessel blood volume, apparent percentage of perfused capillaries, PS products for AIB, and frequency within the endothelium of vesicular profiles.

Aminoisobutyric Acids↗
PubMed1988

Endothelial cell-astrocyte interactions. A cellular model of the blood-brain barrier.

Microvascular endothelial cells in the brain have a number of special properties that underlie formation of the blood-brain barrier (BBB) and contribute to control of the neuronal microenvironment. Evidence from transplantation experiments indicates that signals arising within brain rather than a programmed commitment of the endothelial cells are responsible for the expression of blood-brain barrier properties. The close anatomic relationship between brain endothelial cells and the foot processes of astrocytes suggests a role for astrocytes as a source of the differentiation signals. It is now possible to isolate and separately culture populations of brain-derived endothelial cells and astrocytes. When the two cell types are grown together, a characteristic morphologic organization occurs that is associated with induction of enzymes and tight junctions similar to those found in vivo. Endothelial cells and astrocytes in culture differ in their production of and response to specific polypeptide growth factors. These findings provide the basis for a model of endothelial cell-astrocyte interaction that may explain several aspects of BBB behavior.

Animals↗
PubMed1990

Mechanisms for nonuniform propagation along excitable cables.

We have discussed two classes of mechanisms that can lead to propagation with nonconstant velocity, and to disruption of temporal patterning of action potentials. Inhomogenieties along the cable due to geometrical change or to altered cell coupling can result in conduction delays, with the possibility of block or reflection. Such conduction irregularities have been considered relevant to cardiac reentry phenomena. Our simulations with a discrete number of excitable cells, coupled by gap junctions, showed that the underlying mathematical structure of a saddle point threshold in an ionic model also contributes in an important way to creating a long delay. Such threshold behavior, although not yet demonstrated for some of the most well-studied models of excitability, should not be viewed as extraordinary; we have seen it in models other than those of references 6 and 7, and have produced it in the Hodgkin-Huxley model with reasonable parameter variations (but have not yet checked for reflections with these modifications). We are unaware of any computations with theoretical models of cardiac membrane that yield robust reflection behavior. Perhaps modifications of these models will be necessary in order to obtain adequate delays for reflection. The mechanism we have described here may serve as a guideline for additional features to seek in such parametric tuning. A different class of factors that contribute to interferring with action potential timing include the effects of previous activity on propagation speed. These influences may be described in terms of the dispersion relation, c(T), the dependence of speed on time between action potentials. The form of this function, for large T, reflects the exponential behavior of the action potential's return to rest. Supernormal conduction reveals itself in the dispersion relation when there is an overshoot of excitability in the return to rest, either a single overshoot or an alternating sequence of over- and undershoots (as seen in some nerve membrane models). A simple kinematic recipe was described for quantitatively predicting timing changes during propagation without having to solve the full cable equations. To apply these concepts to cardiac models it will be necessary to compute the dispersion relation for these models. By studying the dependence of c(T) and the waveform trajectory (including conductances as well as membrane potential) on various parameters one may gain insight into the ionic basis for experimentally observed supernormal conduction.

Action Potentials↗
PubMed2002

Time-varying current density distributions in the human heart and brain.

A new method for visualizing and postprocessing three-dimensional time varying vector fields is presented. This method is based on equivalent ellipsoids fitted to these fields. The new technique has been tested on vector fields representing current density reconstruction results based on biomagnetic data from a cardiac patient and a neurological patient. Multiple foci in the vector fields are extracted by multiple ellipsoids which are fitted in an iterative manner. The new method enables visualization of even very complex vector fields, as well as statistical postprocessing.

Brain↗
PubMed2004

Vagal control of the heart: central serotonergic (5-HT) mechanisms.

Cardiac vagal preganglionic neurones (CVPNs) are located within the dorsal vagal nucleus (DVN) and the nucleus ambiguus (nA). In mammals, CVPNs within the nA have small myelinated axons and mediate major chronotropic effects, those in the DVN have non-myelinated axons and mediate smaller chronotropic, dromotropic and inotropic effects. Numerous studies demonstrate important influences of serotonin (5-HT) at multiple sites controlling autonomic outflows including the nucleus tractus solitarius (NTS) where cardiorespiratory afferent fibres terminate, and the CVPNs and rostral ventrolateral medulla (RVLM), the location of sympathetic premotor neurones. We have demonstrated roles for some of the numerous 5-HT receptor subtypes (5-HT1, 5-HT2, 5-HT3, 5-HT4 and 5-HT7) in brainstem regions involved in cardiac control. Intracisternal application of selective ligands was used to study the effect of 5-HT receptors on heart rate and its reflex control. Further electrophysiological studies were also carried out to delineate their location and the mechanisms of action of these ligands. Blocking 5-HT1A receptors attenuated bradycardias evoked by stimulating baroreceptor and cardiopulmonary afferents but not arterial chemoreceptors, whereas antagonizing 5-HT7 receptors markedly attenuated all these reflex bradycardias. Within the DVN, nA and NTS, activation of 5-HT1A receptors could excite or inhibit neurones. In the NTS 5-HT2 receptors also had variable effects; 5-HT2B receptors excite and 5-HT2C receptors inhibit. Antagonism of 5-HT3 receptors attenuated upper airway and cardiopulmonary reflex bradycardias; this is compatible with data showing that 5-HT3 receptors excite DVN and NTS neurones by a glutamate-dependent mechanism. The origin of the glutamate (neuronal or glial) remains unresolved but glia are a possibility as baroreceptor-sensitive NTS neurones receive few direct 5-HT-containing synaptic contacts. Thus, 5-HT plays a critical role in the control of vagal outflow to the heart; however, why so many different receptors are involved, and their relative functional roles, remains unresolved.

Afferent Pathways↗
PubMedDate not supplied

A computational analysis of FXa generation by TF:FVIIa on the surface of rat vascular smooth muscle cells.

A computational model was developed to investigate the contribution of classical mass transport and flow parameters to factor X (FX) activation by the tissue factor-factor VIIa complex (TF:VIIa) on one wall of a parallel-plate flow chamber. The computational results were compared to previously obtained experimental data for the generation of factor Xa (FXa) by TF:VIIa on the surface of cultured rat vascular smooth muscle cells. In this study, the complete steady-state convection-diffusion equation was solved using the commercial software package, FLUENT (Fluent Inc., Lebanon, New Hampshire). A user-defined subroutine interfaced with FLUENT implemented the surface reaction which was modeled using classical Michaelis-Menten reaction kinetics. The numerical solutions were obtained for 12 cases which used combinations of three wall shear rates and four reaction rates. The numerically obtained fluxes for a given reaction rate displayed a wall shear rate dependence which ranged from classical kinetic reaction control (no dependence) to pure diffusional control (maximum dependence). The experimental data, however, were not represented by numerical data generated using a single reaction rate. The three numerically obtained fluxes which corresponded most closely to the experimental fluxes were determined using three different Vmax values. This finding supports the hypothesis that there may be a direct effect of flow on the TF:VIIa complex or the cell membrane.

Algorithms↗
PubMedDate not supplied

Relations between components of impedance cardiogram analyzed by means of finite element model and sensitivity theorem.

The main aim of the study is to establish a relation between different sources of Impedance cardiogram (ICG) as function of spatial distribution of conductivity. A three-dimensional model of a human thorax using the finite element method has been constructed. The model includes 35 horizontal layers consisting of up to 519 pentahedral elements that are automatically divided into tetrahedral ones before calculating the potential distribution. Electrode array configuration proposed by Kubicek et al. (Aerosp. Med. 37: 1208-1212, 1996) has been studied. A relationship proposed by Geselowitz (IEEE Trans. Biomed. Eng. 18: 38-41, 1971) has been used to calculate the sensitivity of the examined electrode array to conductivity changes inside the thorax. This relationship has allowed for the calculation of the contributions to ICG from spatially separated sources when modeling all changes in conductivity simultaneously. It has been confirmed that the main contributions to ICG signal come from ventricles, atria, aorta, and lungs. The relations between these components have been found to be dependent nonlinearly on spatial conductivity distribution. As a result, reliable and reproducible measurements of stroke volume (SV) using ICG are impossible. Nevertheless, ICG can be used to monitor relative changes of SV in all cases where the spatial distribution of conductivity and geometry of the subject, during the examination, is preserved. However, it does not mean that the accuracy of SV measurement will be the same in all these cases.

Biomechanical Phenomena↗
PubMed2001

Modeling advection and diffusion of oxygen in complex vascular networks.

A realistic geometric model for the three-dimensional capillary network geometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to the available morphometric statistics and is supplied by a single arterial source and drains into a pair of venular sinks. We explore steady-state oxygen transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of dissolved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissolved and protein-bound oxygen, and Michaelis-Menten consumption in the parenchymal tissue. The advection velocity field is found by solving the hemodynamic problem for flow throughout the network. The resulting system is described by a set of coupled nonlinear elliptic equations, which are solved using a finite-difference numerical approximation. We find that coupled advection and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially distributed models, and that no "lethal corner," or oxygen-deprived region occurs for physiologically reasonable values for flow and consumption. Concentrations of 0.5-1.0 mM myoglobin facilitate the transport of oxygen and thereby protect the tissue from hypoxia at levels near its P50, that is, when local oxygen consumption rates are close to those of delivery by flow and myoglobin-facilitated diffusion, a fairly narrow range.

Animals↗
PubMed2002

A stochastic nonlinear autoregressive algorithm reflects nonlinear dynamics of heart-rate fluctuations.

Current methods for detecting nonlinear determinism in a time series require long and stationary data records, as most of them assume that the observed dynamics arise only from the internal, deterministic workings of the system, and the stochastic portion of the signal (the noise component) is assumed to be negligible. To explicitly account for the stochastic portion of the data we recently developed a method based on a stochastic nonlinear autoregressive (SNAR) algorithm. The method iteratively estimates nonlinear autoregressive models for both the deterministic and stochastic portions of the signal. Subsequently, the Lyapunov exponents (LE) are calculated for the estimated models in order to examine if nonlinear determinism is present in the deterministic portion of the fitted model. To determine if nonlinear dynamic analysis of heart-rate fluctuations can be used to assess arrhythmia susceptibility by predicting the outcome of invasive cardiac electrophysiologic study (EPS), we applied the SNAR algorithm to noninvasively measured resting sinus-rhythm heart-rate signals obtained from 16 patients. Our analysis revealed that a positive LE was highly correlated to a patient with a positive outcome of EPS. We found that the statistical accuracy of the SNAR algorithm in predicting the outcome of EPS was 88% (sensitivity=100%, specificity=75%, positive predictive value=80%, negative predictive value=100%, p=0.0019). Our results suggest that the SNAR algorithm may serve as a noninvasive probe for screening high-risk populations for malignant cardiac arrhythmias.

Adult↗
PubMed2002

Effect of fluid shear stress on the permeability of the arterial endothelium.

The localization of atherosclerotic lesions is due, in part, to regional variations in the permeability of arterial endothelium to macromolecules. In turn, endothelial permeability may be influenced by fluid shear stresses. The spatial variation in endothelial permeability is reviewed and evidence for shear stress dependence upon permeability is presented. These results are examined in light of various signaling mechanisms that increase permeability by increasing the transport of water and macromolecules through the junctions separating endothelial cells. Signaling pathways cause a change in the dense peripheral band of actin and actin stress fibers or alter the phosphorylation of junction proteins which affects their ability to localize in junctions. Future directions to clarify the effect of shear stress on permeability are considered.

Arteries↗
PubMed2002

Changes of zero-bending-moment states and structures of rat arteries in response to a step lowering of the blood pressure.

There are many papers on tissue remodeling of blood vessels in hypertension, but there are few documents describing the tissue remodeling of the blood vessels following a step lowering of the blood pressure. The present article presents data on the opening angle, the vessel wall thickness, and the thicknesses of the intima-media and adventitia layers of the blood vessels of the lower body (the abdominal aorta, and the common iliac, femoral, saphenous branch, medial plantar, and plantar metatarsal arteries) of the rat after a step lowering of the blood pressure and flow by a controlled constriction of the aorta below both renal arteries. We found a pattern of changes that depend on space (location on the vascular tree), time (after the blood pressure change), and the intensity of disturbance. We model mathematically the dynamics shown by the experimental results by means of the indicial response functions, which are defined as the morphometric changes in response to a step decrease of blood pressure or blood flow. Under the hypothesis that there is a range of linearity between the degree of tissue remodeling and the amplitude of the pressure change, we can use the indicial functions to predict the remodeling of the vessel under an arbitrary history of decreasing blood pressure; and conversely, we can compute the indicial response functions from pertinent results of a single experiment. The totality of all our experiments is consistent with the linearity hypothesis within the range of the experiment. The mathematical analysis and the formulas are presented in the Appendix.

Animals↗
PubMed2003

Estimation of cardiac conduction velocities using small data sets.

Cardiac surface conduction velocities could provide valuable information about the speed and angle of a propagating electrical wave front. It would be advantageous to develop catheter-based velocity mapping devices to improve the visualization of cardiac arrhythmias. However, catheter tip size is limited to < or = 2.5 mm in diameter, restricting the number and size of electrodes that can be placed on a catheter tip. We address the feasibility of estimating conduction speed and angle from small data sets suitable for recording from a catheter device in a standard clinical environment. We estimated cardiac conduction velocities from data subsets of 4-7 closely spaced electrograms, and then compared these estimates to velocities estimated from a larger reference grid. We studied 137 ventricular beats and 17,756 velocity vectors from six swine hearts. Average differences in angle between the two estimates were 0.4 degrees +/- 16 degrees while average differences in speed were 5% +/- 33%. These angle and speed differences provide an initial quantitative assessment of velocity accuracy for the purposes of catheter-based vector mapping.

Animals↗
PubMed2003

Phase response of model sinoatrial node cells.

When a brief current pulse is incident on excitable cells in cardiac and other nervous tissue, a change in phase of the cell's response is usually observed. In cardiac tissue, the cells are exposed to external stimulation of mainly positive currents, which depolarize the cells. We performed a systematic study of the effect of depolarizing stimuli, covering timing, magnitude, and duration, and demonstrated that all of these parameters influence the phase response of the cell. The phase response of our model cell compares favorably with measurements on isolated sinoatrial node cells. We investigated the phase response to single depolarizing stimuli as a function of the stimulus parameters (phase response curves), and then studied cell responses to the combined effect of a pulse train (entrainment phenomena). The range of magnitudes and durations for the stimuli were 0.01-5 nA and 0.01-50 ms. Comparisons of the entrainment properties of the model with experimental results show good agreement with similar modes and different entrainment ratios occurring for similar basic cycle lengths (as functions of the unperturbed cell period). Our results demonstrate that any combination of parameters that provide the same charge transfer to the cell causes a similar phase response, independent of the specific magnitude and duration for the entire range of stimuli investigated.

Action Potentials↗