Dynamics of a three-variable nonlinear model of vasomotion: comparison of theory and experiment.

The effects of pharmacological interventions that modulate Ca(2+) homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca(2+)] in the cytosol, [Ca(2+)] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca(2+) stores and transmembrane ion fluxes via K(+) channels, Cl(-) channels, and voltage-operated Ca(2+) channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca(2+)] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables.

Stress avoidance in a common annual: reproductive timing is important for local adaptation and geographic distribution.

Adaptation to local environments may be an important determinant of species' geographic range. However, little is known about which traits contribute to adaptation or whether their further evolution would facilitate range expansion. In this study, we assessed the adaptive value of stress avoidance traits in the common annual Cocklebur (Xanthium strumarium) by performing a reciprocal transplant across a broad latitudinal gradient extending to the species' northern border. Populations were locally adapted and stress avoidance traits accounted for most fitness differences between populations. At the northern border where growing seasons are cooler and shorter, native populations had evolved to reproduce earlier than native populations in the lower latitude gardens. This clinal pattern in reproductive timing corresponded to a shift in selection from favouring later to earlier reproduction. Thus, earlier reproduction is an important adaptation to northern latitudes and constraint on the further evolution of this trait in marginal populations could potentially limit distribution.

Phosphoramidate derivatives of 2',5'-dideoxyadenosine as potential inhibitors of the EDHF phenomenon.

P-site inhibitors of adenyl cyclase, such as the dideoxynucleosides 2',3'-ddA and 2',5-ddA, have been shown to attenuate EDHF phenomenon in rabbit arteries and veins. In order to present the dideoxynucleosides as pre-activated nucleotides and bypass the kinase, as well as to prevent their metabolism to dideoxyinosine by adenosine deaminase, the aryloxyphosphoramidate approach has been successfully applied, initially on the 2',3'-ddA. In the present work a new series of 2',5'-ddA phosphoramidates has been synthesized, representing the first example of phosphoramidate protide not at the 5'-position.

Deterministic nonlinear characteristics of in vivo blood flow velocity and arteriolar diameter fluctuations.

We have performed a nonlinear analysis of fluctuations in red cell velocity and arteriolar calibre in the mesenteric bed of the anaesthetized rat. Measurements were obtained under control conditions and during local superfusion with NG-nitro-L-arginine (L-NNA, 30 microM) and tetrabutylammonium (TBA, 0.1 mM), which suppress NO synthesis and block Ca2+ activated K+ channels (KCa), respectively. Time series were analysed by calculating correlation dimensions and largest Lyapunov exponents. Both statistics were higher for red cell velocity than diameter fluctuations, thereby potentially differentiating between global and local mechanisms that regulate microvascular flow. Evidence for underlying nonlinear structure was provided by analysis of surrogate time series generated from the experimental data following randomization of Fourier phase. Complexity indices characterizing time series under control conditions were in general higher than those derived from data obtained during superfusion with L-NNA and TBA.

Shil'nikov homoclinic chaos is intimately related to type-III intermittency in isolated rabbit arteries: role of nitric oxide.

We provide experimental evidence for the existence of Shil'nikov homoclinic chaos in the fluctuations in flow which can be observed in isolated perfused rabbit ear arteries, and establish a close association between homoclinicity and type-III Pomeau-Manneville intermittent behavior. The transition between the homoclinic scenario and type-III intermittency is clarified by a mathematical model of the arterial smooth muscle cell. Simulations of the effects of nitric oxide (NO) by the vascular endothelium on these patterns of behavior closely match experimental observations.

Fractal dimensions of laser doppler flowmetry time series.

Laser Doppler flowmetry (LDF) provides a non-invasive method of assessing cutaneous perfusion. As the microvasculature under the probe is not defined the measured flux cannot be given absolute units, but the technique has nevertheless proved valuable for assessing relative changes in perfusion in response to physiological stress. LDF signals normally show pronounced temporal variability, both as a consequence of the pulsatile nature of blood flow and local changes in dynamic vasomotor activity. The aim of the present study was to investigate the use of methods of nonlinear analysis in characterizing temporal fluctuations in LDF signals. Data were collected under standardised conditions from the forearm of 16 normal subjects at rest, during exercise and on recovery. Surrogate data was then generated from the original time series by phase randomization. Dispersional analysis demonstrated that the LDF data was fractal with two distinct scaling regions, thus allowing the calculation of a fractal dimension which decreased significantly from 1.23 +/- 0.09 to 1.04 +/- 0.02 during exercise. By contrast, dispersional analysis of the surrogate data showed no scaling region.

Wavelet and receiver operating characteristic analysis of heart rate variability.

Multiresolution wavelet analysis has been used to study the heart rate variability in two classes of patients with different pathological conditions. The scale dependent measure of Thurner et al. was found to be statistically significant in discriminating patients suffering from hypercardiomyopathy from a control set of normal subjects. We have performed Receiver Operating Characteristc (ROC) analysis and found the ROC area to be a useful measure by which to label the significance of the discrimination, as well as to describe the severity of heart dysfunction.

Universal scaling properties of type-I intermittent chaos in isolated resistance arteries are unaffected by endogenous nitric oxide synthesis.

Spontaneous fluctuations in flow in isolated rabbit ear resistance arteries may exhibit almost-periodic behavior interrupted by chaotic bursts that can be classified as type-I Pomeau-Manneville intermittency. This conclusion was supported by the construction of parabolic return maps and identification of the characteristic probability distributions for the number of oscillations per laminar segment (n) associated with the type-I scenario. Pharmacological inhibition of nitric oxide (NO) synthesis by the vascular endothelium modulated the dynamics of the reinjection mechanism, and thus the generic shape of the probability distribution for n. Nevertheless, average laminar length was related to a derived bifurcation parameter epsilon according to power-law scaling of the form approximately epsilon(beta), where the estimated critical exponent beta was close to the theoretical value of -0.5 both in the presence and absence of NO synthesis.

Gap junction-dependent increases in smooth muscle cAMP underpin the EDHF phenomenon in rabbit arteries.

We have investigated the role of cAMP in nitric oxide (NO)- and prostanoid-independent vascular relaxations evoked by acetylcholine (ACh) in isolated arteries and perfused ear preparations from the rabbit. These EDHF-type responses are shown to be associated with elevated cAMP levels specifically in smooth muscle and are attenuated by blocking adenylyl cyclase or protein kinase A (PKA). Relaxations are amplified by 3-isobutyl-1-methylxanthine, which prevents cAMP hydrolysis, while remaining susceptible to inhibition by the combination of two K(Ca) channel blockers, apamin and charybdotoxin. Analogous endothelium- and cAMP-dependent relaxations were evoked by cyclopiazonic acid (CPA) which stimulates Ca(2+) influx via channels linked to the depletion of Ca(2+) stores. Responses to ACh and CPA were both inhibited by interrupting cell-to-cell coupling via gap junctions with 18alpha-glycyrrhetinic acid and a connexin-specific Gap 27 peptide. The findings suggest that EDHF-type responses are initiated by capacitative Ca(2+) influx into the endothelium and propagated by direct intercellular communication to effect relaxation via cAMP/PKA-dependent phosphorylation events in smooth muscle.

Gap junctional communication underpins EDHF-type relaxations evoked by ACh in the rat hepatic artery.

Synthetic peptides homologous to the Gap 26 and Gap 27 domains of the first and second extracellular loops of the major vascular connexins (Cx37, Cx40, and Cx43) have been used to investigate the role of gap junctions in endothelium-derived hyperpolarizing factor (EDHF)-type relaxations of the rat hepatic artery. These peptides were designated 37,40Gap 26, 43Gap 26, 37,43Gap 27, and 40Gap 27, according to connexin specificity. When administered at 600 microM, none of the peptides individually affected maximal EDHF-type relaxations to ACh. By contrast, at 300 microM each, paired peptide combinations targeting more than one connexin subtype attenuated relaxation by up to 50%, and responses were abolished by the triple peptide combination 43Gap 26 + 40Gap 27 + 37,43Gap 27. In parallel experiments with A7r5 cells expressing Cx40 and Cx43, neither 43Gap 26 nor 40Gap 27 affected intercellular diffusion of Lucifer yellow individually but, in combination, significantly attenuated dye transfer. The findings confirm that functional cell-cell coupling may depend on more than one connexin subtype and demonstrate that direct intercellular communication via gap junctions constructed from Cx37, Cx40, and Cx43 underpins EDHF-type responses in the rat hepatic artery.

Role of phospholipase A(2) and myoendothelial gap junctions in melittin-induced arterial relaxation.

We have used preconstricted rings of rabbit superior mesenteric artery to investigate the contribution of phospholipase A(2) and gap junctional communication to endothelium-derived hyperpolarizing factor (EDHF)-type relaxations evoked by melittin, a polypeptide toxin known to mobilize arachidonic acid from the cell membrane. Arachidonyl trifluoromethyl ketone (30 microM), an inhibitor of the Ca(2+)-dependent phospholipase A(2), and Gap 27 (300 microM), a connexin-mimetic peptide which attenuates intercellular communication via gap junctions, both abolished the endothelium-dependent component of EDHF-type responses evoked by melittin in the presence of the NO synthase inhibitor N(G)-nitro-L-arginine methyl ester (L-NAME, 300 microM) and the cyclooxygenase inhibitor indomethacin (10 microM). By contrast, the sulfhydryl agent thimerosal (300 nM), which amplifies EDHF activity, potentiated nitric oxide (NO)/prostanoid-independent relaxations induced by melittin. Neither arachidonyl trifluoromethyl ketone nor thimerosal modulated relaxations evoked by the peptide toxin in the absence of L-NAME and indomethacin. We conclude that melittin evokes EDHF-type relaxations through activation of the endothelial Ca(2+)-dependent phospholipase A(2) followed by the transmission of a chemical and/or electrical signal via myoendothelial gap junctions. This mechanism of vasorelaxation may be negatively regulated by NO.

Role of gap junctions in endothelium-derived hyperpolarizing factor responses and mechanisms of K(+)-relaxation.

We have examined the effects of ouabain (1 mM), the gap junction inhibitors, 18 alpha-glycyrrhetinic acid (100 microM), N-(piperidin-1-yl)-5-(4-chlorophenyl)-1-(2, 4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxamide hydrochloride (SR141716A; 10 microM) and palmitoleic acid (50 microM), and clotrimazole (10 microM) against endothelium-derived hyperpolarizing factor (EDHF)-mediated and K(+)-induced vasorelaxations in the rat mesentery. In the presence of indomethacin (10 microM) and 300-microM N(G)nitro-L-arginine methyl ester (L-NAME), carbachol caused EDHF-mediated relaxations (R(max)=85.3+/-4.0%). In the presence of ouabain, these responses were substantially reduced (R(max)=11.0+/-2.3%). 18 alpha-glycyrrhetinic acid, SR141716A, palmitoleic acid and clotrimazole also significantly inhibited these EDHF-mediated responses. K(+) caused vasorelaxation of preparations perfused with K(+)-free buffer (R(max)=73.7+/-2.4%), which were reduced by 10-microM indomethacin (R(max)=56.4+/-6.2%). K(+) vasorelaxation was essentially abolished by endothelial denudation. Both ouabain and 18 alpha-glycyrrhetinic acid opposed K(+) relaxations, however, neither SR141716A, clotrimazole nor palmitoleic acid had any effect. Direct cell-cell coupling via gap junctions was attenuated by ouabain, clotrimazole and palmitoleic acid. We conclude that: (i) that gap junctional communication plays a major role in EDHF-mediated relaxations, (ii) that K(+)-vasorelaxation is endothelium-dependent (thus, K(+) is unlikely to represent an EDHF), and (iii) that the inhibitory actions of ouabain and clotrimazole on gap junctions might contribute towards their effects against EDHF.

Numerical study of blood flow in an anatomically realistic aorto-iliac bifurcation generated from MRI data.

Magnetic resonance imaging and computational fluid dynamics (CFD) have been used in combination to simulate flow patterns at the human aorto-iliac bifurcation. Vascular anatomy was reconstructed from stacked two-dimensional (2D) time-of-flight images, and revealed asymmetric, nonplanar geometry with curvature in the abdominal aorta and right iliac artery. The left iliac artery was straight and exhibited a smaller take off angle than the right iliac artery. The anatomical reconstruction was used to generate a computational mesh and obtain CFD predictions of flow and wall shear stress (WSS) within the region of interest. The dynamic boundary conditions necessary were specified by 2D cine phase contrast measurements of velocity profiles in each component vessel. Predicted flow patterns were in good quantitative agreement with experiment and demonstrated major differences in WSS distributions between the iliac arteries. This noninvasive approach has considerable potential to evaluate local geometries and WSS as risk factors for arterial disease in individual subjects.

Comparison of glycyrrhetinic acid isoforms and carbenoxolone as inhibitors of EDHF-type relaxations mediated via gap junctions.

The vascular actions of the lipophilic gap junction inhibitors 18alpha-glycyrrhetinic acid (18alpha-GA), 18beta-glycyrrhetinic acid (18beta-GA) and the water-soluble hemisuccinate derivative of 18beta-GA, carbenoxolone, were investigated in preconstricted rings of rabbit superior mesenteric artery. EDHF-type relaxations to acetylcholine (ACh), observed in the presence of 300 microM NG-nitro-L-arginine methyl ester (L-NAME) and 10 microM indomethacin, were attenuated by preincubation with 18alpha-GA (to 100 microM), 18A-GA (to 10 microM) or carbenoxolone (to 300 microM) in a concentration-dependent fashion. By contrast, none of these agents affected responses to sodium nitroprusside, an exogeneous source of NO, and relaxations evoked by ACh in the absence of L-NAME were attenuated by only approximately 20%. 18alpha-GA exerted no direct effect on vessel tone, whereas 18beta-GA and carbenoxolone caused relaxations which were maximal at approximately 1 and approximately 10 mM, respectively. Relaxations to carbenoxolone were attenuated by endothelial denudation and by incubation with L-NAME, whereas those to 18beta-GA were unaffected. In conclusion, all three agents inhibit EDHF-type relaxations evoked by ACh, providing further evidence for the involvement of gap junctions in such responses. Unlike 18alpha-GA, carbenoxolone and 18beta-GA possess intrinsic vasorelaxant activity which in the case of carbenoxolone involves functional enhancement of NO activity in addition to direct effects on vascular smooth muscle.

Forecasting chaotic cardiovascular time series with an adaptive slope multilayer perceptron neural network.

A multilayer perceptron (MLP) network architecture has been formulated in which two adaptive parameters, the scaling and translation of the postsynaptic function at each node, are allowed to adjust iteratively by gradient-descent. The algorithm has been employed to predict experimental cardiovascular time series, following systematic reconstruction of the strange attractor of the training signal. Comparison with a standard MLP employing identical numbers of nodes and weight learning rates demonstrates that the adaptive approach provides an efficient modification of the MLP that permits faster learning. Thus, for an equivalent number of training epochs there was improved accuracy and generalization for both one- and k-step ahead prediction. The applicability of the methodology is demonstrated for a set of monotonic postsynaptic functions (sigmoidal, upper bounded, and nonbounded). The approach is computationally inexpensive as the increase in the parameter space of the network compared to a standard MLP is small.

Integration of non-linear cellular mechanisms regulating microvascular perfusion.

It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.

Reconstruction of blood flow patterns in human arteries.

Local haemodynamic factors in large arteries are associated with the pathophysiology of cardiovascular diseases such as atherosclerosis and strokes. In search of these factors and their correlation with atheroma formation, quantitative haemodynamic data in realistic arterial geometry become crucial. At present no in vivo non-invasive technique is available that can provide accurate measurement of three-dimensional blood velocities and shear stresses in curved and branching sites of vessels where atherosclerotic plaques are found frequently. This paper presents a computer modelling technique which combines state-of-the-art computational fluid dynamics (CFD) with new noninvasive magnetic resonance imaging techniques to provide the complete haemodynamic data in 'real' arterial geometries. Using magnetic resonance angiographic and velocity images acquired from the aortic bifurcation of a healthy human subject, CFD simulations have been carried out and the predicted flow patterns demonstrate the non-planar-type flow characteristics found in experimental studies.

The endothelial component of cannabinoid-induced relaxation in rabbit mesenteric artery depends on gap junctional communication.

1. We have shown that the endocannabinoid anandamide and its stable analogue methanandamide relax rings of rabbit superior mesenteric artery through endothelium-dependent and -independent mechanisms that are unaffected by blockade of NO synthase and cyclooxygenase. 2. The endothelium-dependent component of the responses was attenuated by the gap junction inhibitor 18alpha-glycyrrhetinic acid (18alpha-GA; 50 microM), and a synthetic connexin-mimetic peptide homologous to the extracellular Gap 27 sequence of connexin 43 (43Gap 27, SRPTEKTIFII; 300 microM). By contrast, the corresponding connexin 40 peptide (40Gap 27, SRPTEKNVFIV) was inactive. 3. The cannabinoid CB1 receptor antagonist SR141716A (10 microM) also attenuated endothelium-dependent relaxations but this inhibition was not observed with the CB1 receptor antagonist LY320135 (10 microM). Furthermore, SR141716A mimicked the effects of 43Gap 27 peptide in blocking Lucifer Yellow dye transfer between coupled COS-7 cells (a monkey fibroblast cell line), whereas LY320135 was without effect, thus suggesting that the action of SR141716A was directly attributable to effects on gap junctions. 4. The endothelium-dependent component of cannabinoid-induced relaxation was also attenuated by AM404 (10 microM), an inhibitor of the high-affinity anandamide transporter, which was without effect on dye transfer. 5. Taken together, the findings suggest that cannabinoids derived from arachidonic acid gain access to the endothelial cytosol via a transporter mechanism and subsequently stimulate relaxation by promoting diffusion of an to adjacent smooth muscle cells via gap junctions. 6. Relaxations of endothelium-denuded preparations to anandamide and methanandamide were unaffected by 43Gap 27 peptide, 18alpha-GA, SR141716A, AM404 and indomethacin and their genesis remains to be established.

Iodinated radiographic contrast media inhibit shear stress- and agonist-evoked release of NO by the endothelium.

1 We have used isolated arterial preparations from the rabbit and dog to investigate whether non-ionic iodinated radiographic contrast media (IRCM) modulate nitric oxide (NO) release. The tri-iodinated monomers iopromide and iohexol were compared with the hexa-iodinated dimer iodixanol. 2 The vasodilator effects of iohexol (300 mg ml-1) and iodixanol (320 mg ml-1) were assessed in cascade bioassay. Increasing concentrations of iohexol or iodixanol caused concentration-dependent relaxations of the detector tissue which were insensitive to 100 microM NG-nitro L-arginine methyl ester (L-NAME) and 10 microM indomethacin, whereas viscosity-associated relaxations induced by the 'inert' agent dextran (MW 80,000; 1-4%) were attenuated by inhibition of NO synthesis. 3 Relaxations of endothelium-intact rings to acetylcholine (ACh) were attenuated by preincubation with iohexol or iodixanol, whereas relaxations to sodium nitroprusside (SNP) in endothelium-denuded rings were unaffected. Inhibitory activity did not correlate with either molarity or iodine concentration. Mannitol caused inhibition of both ACh- and SNP-induced responses. 4 In isolated perfused arteries the depressor responses to iodixanol (320 mg ml-1) and iopromide (300 mg ml-1) administered as close arterial bolus attained a plateau with maximal dilatations of approximately 25% and approximately 60%, respectively. Addition of 100 microM NG-nitro L-arginine (L-NOARG) and/or 10 microM indomethacin to the perfusate had no effect on the responses to either agent. 5 We conclude that IRCM exert direct effects on the endothelium that inhibit NO production rather than its action on vascular smooth muscle. Shear stress-induced stimulation of NO production by IRCM is unlikely to contribute to their vasodilator activity in vivo when administered during angiography despite high intrinsic viscosity.

Minimal model of arterial chaos generated by coupled intracellular and membrane Ca2+ oscillators.

We have developed a mathematical model of arterial vasomotion in which irregular rhythmic activity is generated by the nonlinear interaction of intracellular and membrane oscillators that depend on cyclic release of Ca2+ from internal stores and cyclic influx of extracellular Ca2+, respectively. Four key control variables were selected on the basis of the pharmacological characteristics of histamine-induced vasomotion in rabbit ear arteries: Ca2+ concentration in the cytosol, Ca2+ concentration in ryanodine-sensitive stores, cell membrane potential, and the open state probability of Ca2+-activated K+ channels. Although not represented by independent dynamic variables, the model also incorporates Na+/Ca2+ exchange, the Na+-K+-ATPase, Cl- fluxes, and Ca2+ efflux via the extrusion ATPase. Simulations reproduce a wide spectrum of experimental observations, including 1) the effects of interventions that modulate the functionality of Ca2+ stores and membrane ion channels, 2) paradoxes such as the apparently unpredictable dual action of Ca2+ antagonists and low extracellular Na+ concentration, which can abolish vasomotion or promote the appearance of large-amplitude oscillations, and 3) period-doubling, quasiperiodic, and intermittent routes to chaos. Nonlinearity is essential to explain these diverse patterns of experimental vascular response.