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PubMed1993

Automated flow rate calculations based on digital analysis of flow convergence proximal to regurgitant orifices.

OBJECTIVES: The purpose of the study was to develop and validate an automated method for calculating regurgitant flow rate using color Doppler echocardiography. BACKGROUND: The proximal flow convergence method is a promising approach to quantitate valvular regurgitation noninvasively because it allows one to calculate regurgitant flow rate and regurgitant orifice area; however, defining the location of the regurgitant orifice is often difficult and can lead to significant error in the calculated flow rates. To overcome this problem we developed an automated algorithm to locate the orifice and calculate flow rate based on the digital Doppler velocity map. METHODS: This algorithm compares the observed velocities with the anticipated relative velocities, cos psi/2 pi r2. The orifice is localized as the point with maximal correlation between predicted and observed velocity, whereas flow rate is specified as the slope of the regression line. We validated this algorithm in an in vitro model for flow through circular orifices with planar surroundings and a porcine bioprosthesis. RESULTS: For flow through circular orifices, flow rates calculated on individual Doppler maps and on an average of eight velocity maps showed excellent agreement with true flow, with r = 0.977 and delta Q = -3.7 +/- 15.8 cm3/s and r = 0.991 and delta Q = -4.3 +/- 8.5 cm3/s, respectively. Calculated flow rates through the bioprosthesis correlated well but underestimated true flow, with r = 0.97, delta Q = -10.9 +/- 12.5 cm3/s, suggesting flow convergence over an angle > 2 pi. This systematic underestimation was corrected by assuming an effective convergence angle of 212 degrees. CONCLUSIONS: This algorithm accurately locates the regurgitant orifice and calculates regurgitant flow rate for circular orifices with planar surroundings. Automated analysis of the proximal flow field is also applicable to more physiologic surfaces surrounding the regurgitant orifice; however, the convergence angle should be adjusted. This automated algorithm should make quantification of regurgitant flow rate and regurgitant orifice area more reproducible and readily available in clinical cardiology practice.

Algorithms↗
PubMed2004

Motion of foam films in diverging-converging channels.

Existing theories of the motion of foam films in capillaries often assimilate the pressure drop over the foam films to the static capillary pressure obtained from the Young-Laplace equation. Hence, they ignore the contribution of dynamic effects associated with the rapid stretching and contraction of the foam films to the overall viscous dissipation. This paper reports an investigation of the motion of foam films in axisymmetric diverging-converging channels, taking into account surface viscosity and elasticity. First, a phenomenological theory for the motion of the foam films is developed using simple physical arguments. We show that the displacement of the film obeys a nonlinear second-order differential equation, which can be solved numerically for the (dimensionless) distance from the inlet and the pressure drop as a function of time. Experiments with foam film motion, conducted using glass diverging-converging channels (minimum radius = 3.00 +/- 0,01 mm, maximum diameter = 7,98 +/- 0,01 mm) and nitrogen foam stabilized with sodium dodecyl sulfate (SDS) in brine, are discussed. For a single film motion in the diverging channel, we find that (a) the static pressure drop is a concave-upward function of distance and decreases from 1.0 to about 0.3, whereas (b) the dynamic pressure drop is concave downward and increases from 1 to a maximum of 1.3 and then decreases to 0.7. In the converging channel both the static and dynamic pressure drops are concave-downward functions, but the dynamic pressure drop values are always higher than the static ones. For two films the motions were found to be rather sensitive to the initial arrangement in the channel. The experiments are found to be in excellent agreement with the theoretical predictions. These observations imply that the large flow resistance obtained during foam flow in granular porous media, where converging-diverging channels are abundant, is largely due to the surface elasticity and viscosity of the films.

Journal Article↗
PubMed2006

Effects of mesh style and grid convergence on particle deposition in bifurcating airway models with comparisons to experimental data.

A number of research studies have employed a wide variety of mesh styles and levels of grid convergence to assess velocity fields and particle deposition patterns in models of branching biological systems. Generating structured meshes based on hexahedral elements requires significant time and effort; however, these meshes are often associated with high quality solutions. Unstructured meshes that employ tetrahedral elements can be constructed much faster but may increase levels of numerical diffusion, especially in tubular flow systems with a primary flow direction. The objective of this study is to better establish the effects of mesh generation techniques and grid convergence on velocity fields and particle deposition patterns in bifurcating respiratory models. In order to achieve this objective, four widely used mesh styles including structured hexahedral, unstructured tetrahedral, flow adaptive tetrahedral, and hybrid grids have been considered for two respiratory airway configurations. Initial particle conditions tested are based on the inlet velocity profile or the local inlet mass flow rate. Accuracy of the simulations has been assessed by comparisons to experimental in vitro data available in the literature for the steady-state velocity field in a single bifurcation model as well as the local particle deposition fraction in a double bifurcation model. Quantitative grid convergence was assessed based on a grid convergence index (GCI), which accounts for the degree of grid refinement. The hexahedral mesh was observed to have GCI values that were an order of magnitude below the unstructured tetrahedral mesh values for all resolutions considered. Moreover, the hexahedral mesh style provided GCI values of approximately 1% and reduced run times by a factor of 3. Based on comparisons to empirical data, it was shown that inlet particle seedings should be consistent with the local inlet mass flow rate. Furthermore, the mesh style was found to have an observable effect on cumulative particle depositions with the hexahedral solution most closely matching empirical results. Future studies are needed to assess other mesh generation options including various forms of the hybrid configuration and unstructured hexahedral meshes.

Computer Simulation↗
PubMed1996

Determination of mitral valve area in patients with mitral stenosis by the flow-convergence-region method during changing hemodynamic conditions.

Twenty-eight patients with mitral stenosis underwent Doppler echocardiography at rest and during exercise to determine the accuracy of mitral valve area determination by the flow-convergence-region method during exercise-induced changing hemodynamic conditions. The mitral valve area calculated by using the flow-convergence-region method correlated strongly with that measured by the Gorlin formula both at rest (r = 0.85) and during exercise (r = 0.92) for all 28 patients studied. Although mitral valve area obtained by the flow-convergence-region method did not change (p = 0.1) in 16 patients with echocardiographic mitral scores > or = 12, it increased significantly during exercise (p = 0.0001) in 12 patients with echocardiographic mitral scores < 12. This study suggests that in mitral stenosis, the mitral valve area can be accurately estimated by the flow-convergence-region method both at rest and during changing hemodynamic conditions induced by supine bicycle exercise.

Adult↗
PubMed1997

Requirement for accurate measurement of regurgitant stroke volume by the combined continuous-wave Doppler and color Doppler flow convergence method.

The examination conditions necessary for accurate measurement of regurgitant volume by the proximal flow convergence method applying a simple hemispheric equation remain uncertain. This study investigated the requirement for measuring regurgitant stroke volume from the combined continuous-wave and color Doppler proximal flow convergence approach. Twenty-five pulsatile flow rates were produced by driving five regurgitant stroke volumes ranging from 30 to 70 ml/beat through planar orifices with cross-sectional areas ranging from 0.10 to 1.0 cm2. Four different shaped orifices (circular, rectangular with a major/minor axis ratio 2:1, slitlike with a major/minor axis ratio of 8:1, and square) having identical orifice areas (0.5 cm2) were examined. Regurgitant volume (RV) was estimated from the combined continuous-wave and color Doppler approach according to the previously described equation RV = 2 pi x (r max)2 x AV x (TVI/Vmax), where r max is maximal radial distance, AV is aliasing velocity, TVI is time velocity integral of regurgitant jet, and Vmax is peak velocity of regurgitant jet. Plotting the difference between actual and calculated RV versus radial distance of the proximal convergence shell for each flow rate from circular to rectangular orifices yielded curves conforming to a curvilinear function that crossed the point of zero difference at 1.0 cm. However, in the slitilke orifice, a more remote distance (1.6 cm) is required for the best agreement. Actual regurgitant stroke volume can be estimated well by the combined continuous-wave Doppler and proximal flow convergence method applying a simple hemispheric equation if an aliasing velocity is used that results in a radial distance of at least 1.0 cm.

Confounding Factors, Epidemiologic↗
PubMed2003

Simulating convergent extension by way of anisotropic differential adhesion.

Simulations using the Extended Potts Model suggest that anisotropic differential adhesion can account for convergent extension, as observed during embryonic development of the frog Xenopus laevis for example. During gastrulation in these frogs, convergent extension produces longitudinal tissue growth from latitudinal elongation and migration of aligned constituent cells. The Extended Potts Model employs clustered points on a grid to represent subdivided cells with probabilistic displacement of cell boundaries such that small changes in energy drive gradual tissue development. For modeling convergent extension, simulations include anisotropic differential adhesion: the degree of attachment between adjacent elongated cells depends on their relative orientation. Without considering additional mechanisms, simulations based on anisotropic differential adhesion reproduce the hallmark stages of convergent extension in the correct sequence, with random fluctuations as sufficient impetus for cell reorganization.

Animals↗
PubMed1998

Convergence of simple genetic algorithms for the two-bit problem.

Genetic algorithms (GAs) are stochastic evolutionary algorithms with applications to a variety of optimization problems. The most characteristic novel feature of the GA is that it is based on analogies with the principles of natural biological systems such as natural selection, recombination and mutation. Solving the optimization problem with the GA includes an open fundamental theoretical issue called GA-convergence: (a) what parameters and initial points make the GA converge on a single point? (b) is a GA convergence point an optimal point to the optimization problem? This paper solves these GA-convergence issues mathematically rigorously for the simplest case where the GA consists of two operators analogical with natural selection and recombination, and the optimization problem is the so-called two-bit problem (TBP), the variable consisting of two bits only. Specific results on issue (a) coincide with previous experimental results in GA, while those on issue (b) are significantly new not only in GA but also in population genetics. Moreover, the paper provides a perspective on the generalization of the results for solving the n-bit problem with ordinary simple GAs consisting of the simplest GA plus mutation.

Algorithms↗
PubMed1997

Relationship between mechano-receptive fields of dorsal horn convergent neurons and the response to noxious immersion of the ipsilateral hindpaw in rats.

This study examines the relationship between mechano-receptive fields (inhibitory and excitatory, located on the ipsilateral hindpaw) of convergent dorsal horn neurons, and the responses of the neurons to noxious immersion of an entire paw in noxious hot water. In pentobarbital anesthetized rats with intact spinal cords and in unanesthetized decerebrate-spinalized rats, rat hindpaws were immersed in 50 degrees C water for 10 s after the mechano-receptive fields had been delineated using 5-s noxious pinches. Convergent neurons were either excited or inhibited by noxious immersion of the hindpaw. In both groups, a significant association (chi2, P < 0.01) was found between the make-up of the mechano-receptive field and the response of the neuron to immersion. Immersion-inhibited neurons (intact = 27, spinalized = 13), always had both an excitatory and an inhibitory mechano-receptive field on the same hindpaw. Additionally, when the hindpaw was removed from the noxious water, these immersion-inhibited cells displayed a strong afterdischarge which was immediately inhibited once the paw was reimmersed. Pinch-induced and immersion-induced inhibition were found in both spinalized and intact rats suggesting spinal mechanisms were sufficient to mediate this effect. The majority of immersion-excited cells showed only an excitatory mechano-receptive field on the hindpaw (intact rats = 18/23 or 78.3%, spinalized rats = 24/36 or 66.7%). However, other immersion-excited cells had both an inhibitory and an excitatory mechano-receptive field on the hindpaw (intact rats = 5/23 or 21.7%, spinalized rats = 12/36 or 33.3%). The response of a convergent neuron, which has its excitatory receptive field located on a paw, to noxious immersion of the entire paw can be predicted by the make-up of the mechano-receptive fields. Additionally, since noxious paw immersion affects ipsilateral convergent neurons in two opposite manners, it suggests that other effects, such as heterotopic actions, might also not be uniform.

Animals↗
PubMed1999

Reflex response and convergence of pharyngoesophageal and peripheral chemoreceptors in the nucleus of the solitary tract.

The pharynx is a common conduit for the passage of both ingested material and respiratory gases and may receive a dual control from medullary structures regulating deglutition and respiration. We sought both to compare the pattern of reflex response following stimulation of pharyngoesophageal and peripheral chemoreceptors and to assess whether these afferents converge in the nucleus of the solitary tract. In an arterially perfused working heart-brainstem preparation of mature rat, pharyngoesophageal receptors were stimulated by distension of the pharyngeal-oesophageal junction, whereas chemoreceptors were activated by sodium cyanide solution. In peripheral studies we recorded electromyographic activity from genioglossus, mylohyoideus and the lower thoracic oesophagus as well as hypoglossal, laryngeal and phrenic motor discharge. Sub-glottal pressure was also measured at constant airflow. In central studies, nucleus of the solitary tract neurons were recorded with blind whole-cell techniques. In peripheral studies spontaneous irregular electromyographic discharges (cycle length 99+/-26 s) occurred sequentially in genioglossus and mylohyoideus muscles (during the inter-phrenic nerve activity interval) and subsequently the oesophagus; these were accompanied by post-inspiratory discharges in both hypoglossal and laryngeal motor nerves and an atropine-sensitive bradycardia (-39+/-5 beats/min). Components of the reflex response elicited following stimulation of both pharyngoesophageal receptors and chemoreceptors were qualitatively similar and included: (i) expiratory-related increases in laryngeal pressure; (ii) sequential electromyographic discharge in genioglossus, mylohyoideus muscles and oesophagus; (iii) post-inspiratory burst discharge in hypoglossal, recurrent and superior laryngeal motor nerves; and (iv) an atropine-sensitive bradycardia (-38 to -95 beats/min). The chemoreceptor reflex-evoked responses were abolished after sinoaortic denervation. Of 135 whole-cell recordings of nucleus of the solitary tract neurons, 31 received a synaptic input from pharyngoesophageal receptors (22 excitatory and nine inhibitory). Cells excited by pharyngoesophageal receptor stimulation were either "spontaneously" bursting, which occurred during the inter-phrenic nerve activity interval (cycle length 79+/-22 s; n=9), or non-bursting (n=13). Of the 22 nucleus of the solitary tract neurons excited by pharyngoesophageal receptor stimulation, 77% received a convergent excitatory synaptic input from chemoreceptors (eight bursting and nine non-bursting neurons). Thus, stimulation of pharyngoesophageal receptors and chemoreceptors evoked common reflex response components including activation of hypoglossal, laryngeal adductor, cardiac vagal motoneurons and swallowing. Moreover, some excitatory pharyngoesophageal and chemoreceptors inputs typically converged on nucleus of the solitary tract neurons. The possibility that this convergence manifests a defensive reflex reaction is discussed.

Animals↗
PubMed1999

Monkey insular cortex neurons respond to baroreceptive and somatosensory convergent inputs.

To investigate possible convergence of autonomic and somatosensory input in the insula of the non-human primate, extracellular single-unit recordings were obtained from 81 neurons (43 insular and 38 in surrounding cortex) during application of cutaneous nociceptive stimuli (pinch) and baroreceptor challenge in six anesthetized monkeys (Macaca fascicularis). All cells were also tested with light touch (brush) stimulation. Twenty-six units responded to blood pressure changes; 20 (80%) were identified within the insula (P < 0.001). The majority of these insular units (16/20) also responded to nociceptive pinch (convergent units). More units responsive to changes in blood pressure (unimodal and convergent) were found in the right (18/29, 62%) than in the left insular cortex (2/14, 14%)(P = 0.004). Twenty-nine insular neurons responded to nociceptive stimuli; 16 of these were convergent units and 13 showed unimodal responses to somatosensory stimuli alone. These cells had wide bilateral receptive fields including face, hand, foot and tail. Ten insular neurons were unresponsive to both sets of stimuli (non-responsive cells); significantly more of these cells (28/38) were identified in extrainsular locations (P < 0.01). We suggest that the primate insular cortex may be involved in the integration of cardiovascular function with somatosensory (principally nociceptive) input. This view supports the emerging role of the insular cortex as an important forebrain site of viscerosomatosensory regulation with clinical implications for cardiovascular regulation under conditions of stress and arousal.

Animals↗
PubMed1998

Application of the proximal flow convergence method to calculate the effective regurgitant orifice area in aortic regurgitation.

OBJECTIVES: We sought to determine the reliability of the proximal isovelocity surface area (PISA) method for calculation of effective regurgitant orifice (ERO) of aortic regurgitation (AR). BACKGROUND: The ERO area can be calculated by the PISA method, but this method has not been validated in AR. METHODS: ERO calculation by the PISA method was undertaken prospectively in 71 consecutive patients with isolated AR and achieved in 64 and compared with two simultaneous reference methods (quantitative Doppler and quantitative two-dimensional echocardiography). In addition, this method was compared with angiography in 12 patients, with surgical assessment in 18 patients and with ventricular volumes in all patients. RESULTS: Good correlations between PISA and reference methods were obtained (both r=0.90, both p < 0.0001), but a trend toward underestimation of the ERO by the PISA method was noted (24+/-19 vs. 26+/-22 mm2 and 27+/-23 mm2, respectively, both p=0.04). However, this trend was confined to five patients with an obtuse flow convergence angle (>220 degrees), and on multivariate analysis this variable was the only independent determinant of underestimation of the ERO. In contrast, in 59 patients with a flat flow convergence (< or =220 degrees ), the PISA method, in comparison with reference methods, showed excellent correlations, with a narrow standard error of the estimate (r=0.95, SEE 5.4 mm2, and r=0.95, SEE 5.8 mm2; all p < 0.0001) and no trend toward underestimation (22+/-18 vs. 23+/-16 mm2, p=0.44, and vs. 23+/-18 mm2, p=0.34). CONCLUSIONS: In patients with AR, the PISA method can be used to measure the ERO with reasonable feasibility. Underestimation of the ERO by PISA may occur in patients with an obtuse flow convergence angle. However, in most patients with appropriate flow convergence, PISA provides reliable measurement of the ERO of AR.

Aortic Valve↗
PubMed1997

Dynamical Neural Networks that Ensure Exponential Identification Error Convergence.

Classical adaptive and robust adaptive schemes, are unable to ensure convergence of the identification error to zero, in the case of modeling errors. Therefore, the usage of such schemes to "black-box" identification of nonlinear systems ensures-in the best case-bounded identification error. In this paper, new learning (adaptive) laws are proposed which when applied to recurrent high order neural networks (RHONN) ensure that the identification error converges to zero exponentially fast, and even more, in the case where the identification error is initially zero, it remains equal to zero during the whole identification process. The parameter convergence properties of the proposed scheme, that is, their capability of converging to the optimal neural network model, is also examined; it is shown to be similar to that of classical adaptive and parameter estimation schemes. Finally, it is mentioned that the proposed learning laws are not locally implementable, as they make use of global knowledge of signals and parameters. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.

Journal Article↗
PubMed1998

Evaluating isovelocity surface area flow convergence method with finite element modeling.

Through numerical experimentation we investigated the isovelocity surface area flow convergence method used in estimating regurgitant valve flow rates. Recent advances in three-dimensional color Doppler flow imaging have created renewed interest in this method. Experimentation was based on the use of depth-averaged finite element models of the left heart. The heart models studied varied from "synthetic" representations to a model of a left heart traced from an actual echocardiographic image of a patient with a prolapsed mitral valve. The isovelocity surface area flow convergence method overestimated regurgitant flow rates throughout the Nyquist limits considered with a critical Nyquist limit in which this overestimation is minimized. The angle dependence of Doppler color flow imaging partially corrects for this overestimation. The isovelocity surface area flow convergence method is a viable alternative to methods currently in use. Through numerical experimentation, we have begun to shed light on the inaccuracies inherent in this flow convergence method.

Blood Flow Velocity↗
PubMed2002

On the neuronal basis for multisensory convergence: a brief overview.

For multisensory stimulation to effect perceptual and behavioral responses, information from the different sensory systems must converge on individual neurons. A great deal is already known regarding processing within the separate sensory systems, as well as about many of the integrative and perceptual/behavioral effects of multisensory processing. However, virtually nothing is known about the functional architecture that underlies multisensory convergence even though it is an integral step to this processing sequence. This paper seeks to summarize the findings pertinent to multisensory convergence, and to initiate the identification of specific convergence patterns that may underlie different multisensory perceptual and behavioral effects.

Animals↗
PubMed2003

Semantically convergent and semantically divergent priming in the cerebral hemispheres: lexical decision and semantic judgment.

The effects of semantically divergent and semantically convergent priming on the processing of lexical ambiguity by the two cerebral hemispheres were examined in two visual hemifield experiments. The experiments investigated the ability of the right hemisphere (RH) and the left hemisphere (LH) to summate activation from two single word primes followed by a laterally presented ambiguous target word. In a lexical decision task (experiment 1), the two priming words were either both related to the dominant meaning of the target (new, fresh-NOVEL), or to the subordinate meaning (story, book-NOVEL), or to one dominant and one subordinate meaning (new, story-NOVEL). Results indicated that the LH benefited most from semantically convergent primes that converged onto the dominant meaning of the ambiguous target word, whereas the RH benefited most from semantically mixed (divergent) primes, that diverge on alternate meanings of the ambiguous target word. We used the same stimuli in a semantic relatedness judgment task (experiment 2), and found that the facilitation in the RH was significantly larger when the primes were mixed than when both primes converged on a single (i.e. either dominant or subordinate) meaning of the to-be-presented target word. In contrast, the only facilitation found in the LH was when the two primes were associated with a single meaning (either dominant or subordinate) of the to-be-presented target word. When the primes were mixed, there was no facilitation in the LH. These results support previous findings indicating that during word recognition, the RH activates a broader range of related meanings than the LH, including alternate meanings of ambiguous words. Thus, by summating activation for seemingly incongruous elements, the RH may be critically involved in at least one important component of verbal creativity.

Adolescent↗
PubMed2001

The zebrafish glypican knypek controls cell polarity during gastrulation movements of convergent extension.

Mutations in the zebrafish knypek locus impair gastrulation movements of convergent extension that narrow embryonic body and elongate it from head to tail. We demonstrate that knypek regulates cellular movements but not cell fate specification. Convergent extension movement defects in knypek are associated with abnormal cell polarity, as mutant cells fail to elongate and align medio-laterally. Positional cloning reveals that knypek encodes a member of the glypican family of heparan sulfate proteoglycans. Double mutant and overexpression analyses show that Knypek potentiates Wnt11 signaling, mediating convergent extension. These studies provide experimental and genetic evidence that glypican Knypek acts during vertebrate gastrulation as a positive modulator of noncanonical Wnt signaling to establish polarized cell behaviors underlying convergent extension movements.

Amino Acid Sequence↗
PubMed2003

Distributions of wall shear stress in venular convergences of mouse cremaster muscle.

OBJECTIVE: Wall shear stress regulates a variety of vascular functions and can be affected by variations in blood viscosity and wall shear rate independently. Therefore, the distribution of wall shear stress was characterized in converging flow regions of postcapillary venules to identify the relative contributions of shear rate and viscosity to wall shear rate and to determine whether venular branching directly affects the local shear environment. METHODS: Blood viscosity was evaluated as a function of vessel diameter and hematocrit, determined from fluorescent red blood cell (RBC) flux. Wall shear rate was measured directly from velocity profiles acquired using fluorescent RBC tracking or was estimated assuming Poiseuille flow conditions. Wall shear stress was calculated for measurements made across regions of converging flow. RESULTS: Measurements of wall shear stress showed no significant variation with location across the convergence (p < 0.9). Measures of viscosity showed little variation, for local measures of hematocrit (2.9 +/- 0.1 cp; coefficient of variation [CV]: 12%) or systemic hematocrit (3.4 +/- 0.1 centipoise [cp]; CV: 14%). Measures of wall shear rate showed greater variability for both direct measurements (61.2 +/- 8.7s; CV: 92%) and estimates assuming Poiseuille flow (122.7 +/- 15.7 s; CV: 83%). CONCLUSIONS: Variations in wall shear stress are independent of location through a venular convergence in contrast to arteriolar bifurcations. In addition, wall shear rate is significantly more variable than viscosity and, therefore, primarily accountable for wall shear stress variations in postcapillary venules.

Animals↗
PubMed2004

Convergence of the natural approximations of piecewise monotone interval maps.

We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which is Lipshitz continuous and for which the densities converge in the bounded variation norm at a logarithmic rate. This shows that in general one cannot expect exponential convergence in the bounded variation norm. Here we prove that if the derivative of the interval map is Holder continuous and its variation is well approximable (gamma-uniform variation for gamma>0), then the densities converge exponentially fast in the norm.

Journal Article↗