Nonsymmetrical bifurcations in arterial branching

The results of optimality studies of the branching angles of arterial bifurcations are extended to nonsymmetrical bifurcations. Predicted nonsymmetrical bifurcations are found to be not unlike those observed in the cardiovascular system.     

Optimality principles in arterial branching

A comparative study of four optimality principles for the branching geometry of blood arteries is presented. The results offer four different criteria which can be tested by experimental data to establish which of these principles is followed in the cardiovascular system. More significantly, the results suggest the further possibility that the geometry of arterial junctions may be governed by all of these principles simultaneously, to thus achieve a much higher degree of optimality than has hitherto been suspected. This result offers a basis for seeking a correlation between the degree of optimality of a particular junction and the incidence of certain arterial lesions at that junction.     

Three-dimensional aspects of arterial branching

Arterial junctions give rise to different images when viewed from different directions. When a two-dimensional bifurcation is viewed in a direction other than normal to its branching plane, the branching angles will be distorted and the resulting picture will not be a true picture of that bifurcation. If the bifurcation is three-dimensional, some distortions will occur no matter which way the bifurcation is viewed. These distortions are analyzed for a wide range of situations and data is provided from which the corresponding errors can be estimated.     

Local geometry of arterial branching

A model of the geometrical structure of arterial bifurcations is proposed in the context of optimality of the bifurcation as a fluid conducting system. Optimality is considered both globally, in terms of the cardiovascular system as a whole, and locally, in terms of the orderliness of the flow in the bifurcation region. It is shown that a bifurcation can be optimal both globally and locally. Typical examples of such bifurcations are given.     

The role of shear forces in arterial branching

A new optimality principle for the branching angles of blood vessels in the cardiovascular system is proposed: the principle of minimum drag. The results are examined in the light of general observations and compared with those obtained from the principles of minimum work and minimum volume. It is shown that in some aspects the new principle is equally consistent with observations, and, in other aspects, it is perhaps more plausible than the other two principles.     

Cost of departure from optimality in arterial branching

Measurements of branching angles in the arterial tree have in the past indicated a great deal of scatter away from what is expected to be optimum on theoretical grounds. In this study the cost penalty of nonoptimum branching angles is calculated for the first time to determine how far from optimum these angles are. The results lead to the remarkable conclusion that while the scatter of the measured branching angles is fairly large, they represent deviations from optimum angles which correspond to only 2% or so penalty in cost.     

Encoding power in communication networks

In animal societies, conflicts can be resolved by combatants or through third-party intervention. In gregarious species, conflicts among pairs can spread to involve multiple individuals. In the case of large conflicts, containment and termination of aggression by third parties is important. Successful intervention relies on consensus among combatants about the intervener's capacity to use force. We refer to this consensus as power. We measure it and study how it arises, using as our model system a pigtailed macaque (Macaca nemestrina) society. In macaques, the degree to which one individual perceives another as capable of using force is communicated using a special dominance signal. Group consensus about an individual's capacity to use force arises from the network of signaling interactions. We derive a formalism to quantify consensus in the network. We find that the power distribution is fat tailed and power is a strong predictor of social variables including request for support, intervention cost, and intensity. We develop models to show how dominance-signaling strategies promote robust power distributions despite individual signaling errors. We suggest that when considering correlated interactions among many individuals it can be more useful to emphasize coarse-grained information stored at the group level--behavioral macrostates--over detailed information at the individual level.     

Hydrodynamics of arterial branching--the effect of arterial branching on distal blood supply

A study was conducted to investigate the hydrodynamics of branching flow in relation to the blood supply to the basal part of the brain. A series of measurements of the branching loss-coefficients under laminar steady flow were conducted using model branches with various geometries, and the effect of branching on blood supply to distal areas was described using a lumped-parameter model of the vascular structure. It was revealed that in the blood circulation, branching loss is important where a small artery divides off with a large branching angle from a large trunk. It was also indicated that the effect of such branching on the distal blood supply might become more significant when the peripheral resistance is reduced, thereby increasing the blood velocity in the trunk.     

Selective regulation of arterial branching morphogenesis by synectin

Branching morphogenesis is a key process in the formation of vascular networks. To date, little is known regarding the molecular events regulating this process. We investigated the involvement of synectin in this process. In zebrafish embryos, synectin knockdown resulted in a hypoplastic dorsal aorta and hypobranched, stunted, and thin intersomitic vessels due to impaired migration and proliferation of angioblasts and arterial endothelial cells while not affecting venous development. Synectin(-/-) mice demonstrated decreased body and organ size, reduced numbers of arteries, and an altered pattern of arterial branching in multiple vascular beds while the venous system remained normal. Murine synectin(-/-) primary arterial, but not venous, endothelial cells showed decreased in vitro tube formation, migration, and proliferation and impaired polarization due to abnormal localization of activated Rac1. We conclude that synectin is involved in selective regulation of arterial, but not venous, growth and branching morphogenesis and that Rac1 plays an important role in this process.     

Cell communication networks in cancer invasion

The invasion of cancer is a major clinical problem. It is now apparent that invasion is not a simply a cancer cell autonomous process but relies on a complex network of paracrine interactions. Furthermore, this network can change as cancer cells disseminate. Here we summarise the key components of the network and their mechanisms of communication. Finally, we discuss the difficulties and opportunities that this complex network of interactions presents during cancer therapy.     

The branching angles in computer-generated optimized models of arterial trees

The structure of a complex arterial tree model is generated on the computer using the newly developed method of "constrained constructive optimization." The model tree is grown step by step, at each stage of development fulfilling invariant boundary conditions for pressures and flows. The development of structure is governed by adopting minimum volume inside the vessels as target function. The resulting model tree is analyzed regarding the relations between branching angles and segment radii. Results show good agreement with morphometric measurements on corrosion casts of human coronary arteries reported in the literature.     

Correlated dynamics in egocentric communication networks

We investigate the communication sequences of millions of people through two different channels and analyse the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his/her several neighbours, thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constraints (for short messages) and partly to the human behavioural features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics.     

A generalization of the optimal models of arterial branching

Optimal models of arterial branching angles are usually based on the assumption that the equation relating flow and radius is given byf=kr ³, as proposed by Murray in 1926. An exception is the model of Uylings (1977), in which he allowed the exponent ofr to vary from 2.33 to 3.0. Theoretical considerations coupled with empirical evidence suggest that the cubic flow equation may not be appropriate to describe the branching pattern of the arterial tree. The optimal models are modified to accommodate a more general flow equationf=kr ^x . Models that minimize a geometric feature such as surface or volume are sensitive to variations inx in a different way from those which minimize flow-related parameters, such as power loss due to friction and shear stress.     

Dominance of geometric overelastic factors in pulse transmission through arterial branching

The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.     

Electrical current and cAMP induce lateral branching in the stolon of hydroids

Pulses of cAMP injected ionophoretically or mechanically into the epidermis of the stolon of the hydroid Hydractinia induce lateral branching at the site of stimulation. Up to 72% of the punctured loci developed a bud 6–24 hr after stimulation. Only pulsatile injection in periods of, e.g., 5 min is effective in inducing lateral buds. Controls provided evidence that in the ionophoretic mode the inducing effect derives not only from the cAMP signal but also, in part, from the positive electric current passed through the micropipet during the retention interval: DC (e.g., 8 nA × 1 hr or 20 nA × 2 hr) entering the tissue also evokes a positive response. Additional pulses of cAMP, but not of AMP, enhance the current effect. The threshold dose for a significant amplification has been determined to be 3.6 × 10^?13M (18 pulses à 2 × 10^?14M).     

A model for renal arterial branching based on graph theory

The kidney is one of the most complicated organs in terms of structure and physiology, in part because it is highly vascularized. The renal vascular development occurs through two mechanisms that sometimes overlap: vasculogenesis and angiogenesis. Here, we consider angiogenesis to model the renal arterial tree with the two processes of vascular angiogenesis: sprouting and splitting. We recognize the vessels are not tubes with ends that get glued but physiological factors are relevant into the vascular development. Our contribution integrates the graph theory and physiological information to derive a quantitative model for the vascular tree in the sense that the vertices and edges represent, respectively, a branching point and a vessel. From such a premise, development of the arterial vascular tree of the kidney is mathematically expressed, including physiological processes as the effect of the vascular endothelial growth factor (VEGF) on the vessel length. A definition of the graph is used to visualize the topology of vascular tree in kidney providing physiological information into the edges. Thus, renal arterial branching is modeled as a graph where edges are labeled and oriented.     

Comparison of steady and pulsatile flow in a double branching arterial model

Data are presented to compare fluid flow parameters for steady flow with those for time-varying flow in a simplified two branch model which simulates the region of the abdominal aorta near the celiac and superior mesenteric branches of the dog. Measurements in the model included laser doppler anemometry velocity profiles during steady flow, sinusoidal flow with a superimposed mean flow (referred to as simple oscillatory flow) and arterial pulsatile flow. Shear rate measurements were made by an electrochemical technique during steady flow. Flow visualization studies were done during steady and pulsatile flow. Fluid flow effects in the simplified model during steady flow showed many similarities to the results from previous steady flow studies in a canine aortic cast. Shear rates in the region of the proximal (first, or celiac) branch were independent of flow rates in the distal (second, or mesenteric) branch, but the shear pattern within the proximal branch changed significantly as flow in the proximal branch increased. Shear rates on the proximal flow divider (leading edge into the distal branch) depended primarily on the flow rate to the proximal branch, but not on flow to the distal branch. At certain daughter branch flow ratios (approximately 2:1, proximal to distal), flow separation was promoted at the outer wall of the second branch, but flow separation did not occur in the first branch. In contrast to the canine aortic case results, flow separation was never detected on the distal (mesenteric) flow divider of the simplified model. This observation reflects the subtle effects of geometry on flow since the mesenteric flow divider in the canine cast protrudes into the main flow whereas the distal flow divider in the simplified model does not. There were distinct differences in the flow phenomena between steady, simple oscillatory and arterial pulsatile flow. Peak shear rates during pulsatile flow were as much as 10--100 times greater than steady flow shear rates at comparable mean flow rates. Particularly noteworthy for the pulsatile flow with a Womersley parameter of sixteen were very blunt velocity profiles throughout systole, and the absence of flow separation or reversal in those regions of the model that exhibited flow separation during steady flow. The shape of the waveform influences the nature of the flow during time-varying flows. Future studies of fluid dynamics in model systems must consider the pulsatile nature of the flow if a true interpretation of arterial flow phenomena is to be made.