Branching Asymmetry Research Articles

Species-Specific Pulmonary Arterial Asymmetry Determines Species Differences in Regional Pulmonary Perfusion

The functional significance of differences in pulmonary vascular branching and diameter asymmetry between the human and quadruped lung has not previously been addressed. To evaluate the contribution of branching asymmetry to observable species differences in blood flow gradients, computed distributions of blood flow were compared in structure-based models of the human and ovine pulmonary arteries. The models were derived using a combination of computed tomography and a volume-filling algorithm. Pressure, flow, and deformed vessel diameter were calculated in both species models using equations representing conservation of mass and momentum, and a pressure-diameter relationship. The major difference between the human and ovine results was the presence of a large region of "zone 4" flow and higher mean flows in the central region of the ovine lung compared to that in the human. Heterogeneity in tissue perfusion and the contribution of gravity were similar in both species models; however, the gravitationally directed gradients of perfusion in the human and ovine models were different and each consistent with human and quadruped measurements, respectively. The results suggest that measured species differences in pulmonary perfusion gradients are largely determined by differences in branching asymmetry.

Axial-vector meson emitting weak nonleptonic decays of bottom baryons

We investigate the two-body weak nonleptonic decays of ${\ensuremath{\Lambda}}_{b}^{0}$, ${\ensuremath{\Xi}}_{b}^{0}$, and ${\ensuremath{\Xi}}_{b}^{\ensuremath{-}}$ into the octet baryons (${J}^{P}=1/{2}^{+}$) and axial-vector mesons (${J}^{P}={1}^{+}$) employing the factorization scheme and obtain their branching ratios and asymmetry parameters.

First estimate of axial-vector meson emitting weak nonleptonic decays of charm baryons based on the factorization scheme

We investigate the weak nonleptonic decays of ${\ensuremath{\Lambda}}_{c}^{+}$, ${\ensuremath{\Xi}}_{c}^{+}$, and ${\ensuremath{\Xi}}_{c}^{0}$ into the octet baryons (${J}^{P}=1/{2}^{+}$) and axial-vector mesons (${J}^{P}={1}^{+}$) employing the factorization scheme and predict their branching ratios and asymmetry parameters.

Ureteric branching morphogenesis in BMP4 heterozygous mutant mice

Exogenous bone morphogenetic protein 4 (BMP4) inhibits ureteric branching morphogenesis and amplifies the already existing branching asymmetry in the developing mouse kidney in vitro. In the present study we examined ureteric branching morphogenesis in BMP4/lacZ heterozygous (BMP4(+/-)) mice in vitro under control conditions and in the presence of exogenous BMP4 using three-dimensional image analysis software. The relative expression of BMP4 mRNA was determined in BMP4(+/-) and wildtype urogenital ridges using real-time PCR. Embryonic day 12.5 (E12.5) BMP4(+/-) and wildtype mouse metanephroi were cultured for 48 h with or without 260 ng mL(-1) recombinant human BMP4 (rhBMP4) and were then wholemount immunostained in order to identify the ureteric epithelium, which was quantified in three dimensions. Despite a significant reduction in BMP4 mRNA in BMP4(+/-) mice, qualitative and quantitative studies identified no differences in ureteric branching morphogenesis between phenotypically normal BMP4(+/-) and wildtype metanephroi in either BMP4-treated or control cultures. Both BMP4(+/-) and wildtype metanephroi cultured in the presence of BMP4 showed a decrease in total ureteric length, branch number and ureteric volume, and increased average branch length compared with control cultures. A marked anterior-posterior asymmetry in both ureteric length, branch number and average branch length was observed in BMP4-treated metanephroi from both genotypes. A similar asymmetry was revealed in control metanephroi from both genotypes. This asymmetry is the result of reduced ureteric branching morphogenesis but not elongation in the posterior region of the kidney. These results suggest that despite reduced endogenous BMP4 mRNA levels, most BMP4(+/-) embryos can still facilitate normal ureteric branching morphogenesis during development. In addition, reduced endogenous levels of BMP4 do not alter the inhibitory effects of exogenous BMP4 on ureteric branching or amplification of normal renal asymmetry.

Relating Airway Diameter Distributions to Regular Branching Asymmetry in the Lung

We study the distribution Pi(n)(D) of airway diameters D as a function of generation N in asymmetric airway trees of mammalian lungs. We find that the airway bifurcations are self-similar in four species studied. Specifically, the ratios of diameters of the major and minor daughters to their parent are constants independent of N until a cutoff diameter is reached. We derive closed form expressions for Pi(N)(D) and examine the flow resistance of the tree based on an asymmetric flow division model. Our findings suggest that the observed diameter heterogeneity is consistent with an underlying regular branching asymmetry.

CT-based geometry analysis and finite element models of the human and ovine bronchial tree.

The interpretation of experimental results from functional medical imaging is complicated by intersubject and interspecies differences in airway geometry. The application of computational models in understanding the significance of these differences requires methods for generation of subject-specific geometric models of the bronchial airway tree. In the current study, curvilinear airway centerline and diameter models have been fitted to human and ovine bronchial trees using detailed data segmented from multidetector row X-ray-computed tomography scans. The trees have been extended to model the entire conducting airway system by using a volume-filling algorithm to generate airway centerline locations within detailed volume descriptions of the lungs or lobes. Analysis of the geometry of the scan-based and model-based airways has verified their consistency with measures from previous anatomic studies and has provided new anatomic data for the ovine bronchial tree. With the use of an identical parameter set, the volume-filling algorithm has produced airway trees with branching asymmetry appropriate for the human and ovine lung, demonstrating the dependence of the method on the shape of the lung or lobe volume. The modeling approach that has been developed can be applied to any level of detail of the airway tree and into any volume shape for the lung; hence it can be used directly for different individuals or animals and for any number of scan-based airways. The resulting models are subject-specific computational meshes with anatomically consistent geometry, suitable for application in simulation studies.

Branching tree model with fractal vascular resistance explains fractal perfusion heterogeneity.

Perfusion heterogeneities in organs such as the heart obey a power law as a function of scale, a behavior termed "fractal." An explanation of why vascular systems produce such a specific perfusion pattern is still lacking. An intuitive branching tree model is presented that reveals how this behavior can be generated as a consequence of scale-independent branching asymmetry and fractal vessel resistance. Comparison of computer simulations to experimental data from the sheep heart shows that the values of the two free model parameters are realistic. Branching asymmetry within the model is defined by the relative tissue volume being fed by each branch. Vessel ordering for fractal analysis of morphology based on fed or drained tissue volumes is preferable to the commonly used Strahler system, which is shown to depend on branching asymmetry. Recently, noninvasive imaging techniques such as PET and MRI have been used to measure perfusion heterogeneity. The model allows a physiological interpretation of the measured fractal parameters, which could in turn be used to characterize vascular morphology and function.

Predicting root biomass from branching patterns of Douglas‐fir root systems

There are many examples of branching networks in nature, such as tree crowns, river systems, arteries and lungs. These networks have often been described as being self‐similar, or following scale‐invariant branching rules, and this property has been used to derive several scaling laws. In this paper we model root systems of Douglas‐fir (Pseudotsuga menziesii var. glauca (Beissn.) Franco) as branching networks following several simple branching rules. Our objective is to establish a relationship between trunk diameter and root biomass. We explore the effect of the self‐similar branching assumption on this relationship. Using data collected from a mature stand in British Columbia, we find that branching asymmetry and the rate of root taper change with root size, thereby violating the assumption of self‐similarity. However, the data are in general agreement with Leonardo da Vinci's area‐preserving branching hypothesis. We use the field data to parameterize two models, one assuming self‐similar branching and a second incorporating the measured size dependencies of branching parameters. The two models differ by only a small amount (≈8%) in their predictions. For both models, the predicted relationship between trunk diameter and root biomass is in good concordance with previously published empirical data. We conclude that the assumption of self‐similar branching, although violated by the data, nevertheless provides a useful tool for predicting the allometric relationship between trunk diameter and root biomass. Finally, we use our models to show that the geometric properties of individual bifurcations fundamentally change the root biomass cost of different root topologies.

Airway branching morphology of mature and immature rabbit lungs.

The scheme of Horsfield et al. for describing the pulmonary airway tree (J Appl Physiol 52: 21-26, 1982) catalogs each airway according to its order and the difference in order of its two daughters (denoted Delta). Although this scheme captures the natural asymmetry in the airway tree, it is still deterministic, because it assumes that all airways of a given order are the same; yet such variability is extremely important in determining the overall behavior of the lungs. We therefore analyzed complete lung lobes from three mature and two immature rabbits and determined the Horsfield order and Delta of every airway down to the terminal bronchioles. We also measured the diameter of each airway. This allowed us to determine the average structure of the rabbit airway tree, the variation about this average, and also how the structures of mature and immature airway trees compare. We found some variation in branching asymmetry and airway diameter at a given order between animals but no evidence of systematic differences in structure between mature and immature lungs. We found evidence of a difference in the branching structure of the peripheral vs. the central part of the airway tree (the break point being around order 20). We also determined the nature of the variation in Delta and diameter as a function of order, which should be valuable for the development of computer models seeking to encapsulate the naturally occurring regional variation in airway geometry in the normal rabbit lung.

STUDY OF TWO-BODY HADRONIC DECAYS OF Λb BARYON IN THE HEAVY QUARK EFFECTIVE THEORY

We investigate the two-body nonleptonic weak decays of Λb baryon into a Λc baryon and a pseudoscalar or vector meson in the framework of HQET. With the additional assumption of factorization the branching ratios and asymmetry parameters for various decay processes [Formula: see text] are obtained. Treating the s quark as heavy we have also applied HQET to study the decay process Λb→ΛJ/ψ and the estimated branching ratio for this process is lying within the present experimental limits.

Simulated distributions of the density of cell adhesion molecules over branching processes with different geometry and intracellular trafficking

Adhesive cell-cell and cell-substrate interactions mediated by different types of cell adhesion molecules (CAM) are important for growth and migration processes. In simulation study we investigated the impact of geometry of branching cellular processes on the lateral distribution of CAM due to retrograde lateral diffusion from a growing part, where they were delivered by different assumed types of trafficking. The model incorporates trafficking of CAM to and installation in the growing active part of the cell, their lateral diffusive redistribution, formation and dissociation of CAM/ligand complexes, and CAM internalization by endocytosis. Since the rate of growth is two and one order(s) of magnitude slower than the rate of trafficking and lateral diffusion, respectively, steady state distributions of CAM were considered. Three possible types of intracellular CAM partitioning between sister branches were considered: equal, proportional to the branch cross-section area, and proportional to the branch surface area. Asymmetry of branching led to various inhomogeneous distributions of the CAM surface density along the branches, and these distributions depended on the type of intracellular trafficking, which might provide a basis for different modes of growth. One can speculate that, depending on these modes, initially asymmetrical branching can be either reinforced or symmetrized during further development.

Is local metabolism the basis of the fractal vascular structure in the heart?

The distribution of blood flow in the heart muscle is very heterogeneous and shows a self-similar fractal pattern, extending to small spatial scales. It is very likely that local oxygen consumption is more or less proportional to local blood flow and that local aerobic metabolism also is very heterogeneous. It is not yet clear whether local metabolism is heterogeneous in origin and the distribution of flow has secondarily adapted to metabolism, or, the other way around, whether flow is primarily heterogeneous because of the irregular structure of the coronary tree and flow has adapted to metabolism. Little is known yet about the developmental and adaptive mechanisms which bring about mutual adjustment between vascular growth and local metabolic demand, and genes and growth factors involved in shaping the structure of the coronary tree have only begun to be identified. Fractal and nonlinear dynamic mathematical models generate complex heterogeneous structures from simple nonlinear deterministic rules which are recursively applied. Such nonlinear models may thus help to explain the generation of large vascular trees regulated by synergy of a limited number of genes and signaling molecules. This may explain the relative regularity of space filling of the vascular tree and the asymmetry of branching and flow distribution in the tree.

Input impedance and reflection coefficient in fractal-like models of asymmetrically branching compliant tubes.

A mathematical model is described, based on linear transmission line theory, for the computation of hydraulic input impedance spectra in complex, dichotomously branching networks similar to mammalian arterial systems. Conceptually, the networks are constructed from a discretized set of self-similar compliant tubes whose dimensions are described by an integer power law. The model allows specification of the branching geometry, i.e., the daughter-parent branch area ratio and the daughter-daughter area asymmetry ratio, as functions of vessel size. Characteristic impedances of individual vessels are described by linear theory for a fully constrained thick-walled elastic tube. Besides termination impedances and fluid density and viscosity, other model parameters included relative vessel length and phase velocity, each as a function of vessel size (elastic nonuniformity). The primary goal of the study was to examine systematically the effect of fractal branching asymmetry, both degree and location within the network, on the complex input impedance spectrum and reflection coefficient. With progressive branching asymmetry, fractal model spectra exhibit some of the features inherent in natural arterial systems such as the loss of prominent, regularly-occurring maxima and minima; the effect is most apparent at higher frequencies. Marked reduction of the reflection coefficient occurs, due to disparities in wave path length, when branching is asymmetric. Because of path length differences, branching asymmetry near the system input has a far greater effect on minimizing spectrum oscillations and reflections than downstream asymmetry. Fractal-like constructs suggest a means by which arterial trees of realistic complexity might be described, both structurally and functionally.

Measurements of the magnetic moment of the $$\Sigma ^ + and \bar \Sigma ^ - $$ hyperons and of hyperon radiative decayshyperons and of hyperon radiative decays

We have made a high-precision measurement of the magnetic moment of the Σ+ hyperon, using the precession of the spin in a conventional magnetic field. We have also made the first measurement of the magnetic moment of its antiparticle, the\(\bar \Sigma \). In a separate experiment, we have demonstrated the precession of spin during channelling in a bent crystal, allowing a complementary measurement of the Σ+ magnetic moment. This technique has promise for the measurement of magnetic moments of charmed baryons. We also present results on the branching ratio and asymmetry parameter in the decay Σ+→pγ, and studies of the decays Σ-→pγ and Ξ-→Σ-γ.

Asplenia syndrome: Insight into embryology through an analysis of cardiac and extracardiac anomalies

Asplenia syndrome is characterized by complex congenital heart defects, asplenia and abdominal heterotaxy. Recent interest in the syndrome has been increased by new knowledge arising from animal models and by continuing improvements in surgical outcome in childhood. To further elucidate the embryologic timing and mechanisms of the asplenia syndrome, 32 necropsy cases were reviewed and 487 published autopsy cases were reanalyzed at the hospital. The most common congenital heart defects were atrial septal defects, common atrioventricular canals and conotruncal anomalies. With use of current information on the timing of normal development, it was hypothesized that most defects originate at Streeter Horizon XIII; patients averaged 3.2 Horizon XIII defects, more than at any other stage. Distribution was unimodal. Extracardiac anomalies also exhibited a developmental spectrum. Because the normal spleen develops by Horizon XIII, asplenia, the sine qua non of the syndrome, originates then or earlier. Abnormal pulmonary location occurred in 80% of cases, with right isomerism occurring most often; pulmonary branching asymmetry also originates at or before Horizon XIII. Abdominal heterotaxy occurred in 72% of cases, but the timing of origin is unclear. Anomalies of other systems, including genitourinary, musculoskeletal, endocrine, and nervous systems, develop later (typically XV to XXIII); specific anomalies were less frequent, although much more prevalent than in the general population. It is concluded that asplenia syndrome is a focal developmental disturbance in laterally which occurs primarily at Horizon XIII.

On the asymmetry of the primary branching of vagal sensory axons: possible role of the supporting tissue.

Central and peripheral nonmedullated processes of vagal nodosal neurons of the cat were studied in normal nerves and after regeneration along their anatomical course and along the hypoglossal nerve. Nonmedullated fibers above the ganglion and in the root had comparable sizes (approximately 0.37 micron2) and caliber distribution. Below the ganglion, the cross-sectional area increased to 1.0 micron2. In axons of equal caliber, supranodosal and radicular fibers had similar microtubular densities while infranodosal fibers had two- to threefold that of the former. Regenerated fibers were studied after a recovery period of 6-9 months. Regrown axons were smaller than their parent axons; in turn, these were smaller than normal axons. This holds for central and peripheral nodosal branches, for homologous and heterologous regeneration. Regrown peripheral branches, either along their anatomical pathway or along the hypoglossal nerve, showed no change in microtubular density. Central branches exhibited their characteristic microtubular content when they regenerated along their anatomical course, but when regrowth took place along the hypoglossal nerve, the original low microtubular content of these branches increased to match the high content of peripheral fibers; parent central axons also shifted their microtubular content toward the pattern of peripheral fibers. We propose that the supporting tissue participates in specifying the organization of axonal microtubules.

Guided-wave Electro-optic X-type Switches: Symmetry, Switching Characteristics and Cross-talk

Abstract The influence of branching asymmetry and electrode offset on the switching characteristics and cross-talk of X-type switches is analysed theoretically. The relationship between the switch symmetry (i.e. the existence of a plane or centre of inversion) and the switching characteristics is found. Cross-talk levels of slightly asymmetric Ti:LiNbO3 switches are calculated.

Model analysis of intra-acinar gas exchange

A previously described multibranch-point model, incorporating branching asymmetry within an acimus, has been extended to include gas exchange at the alveolar surface. Using a transport equation for simultaneous convection and diffusion within the gas phase and independent perfusion of all nodes, we obtained steady-state solutions for the temporal an spatial distributions of O 2 and CO 2 tensions within an acinus during a respiratory cycle. Results for conditions corresponding to both rest and moderate exercise indicated a significant inhomogeneity of ags concentrations within a single acinus. The coefficient of variation of PA CO 2 at end-inspiration during exercise reached 11.3%. Despite this non-uniformity the computation of a negligible PA O 2 Pa O 2 difference indicated no impairment in gas exchange. The simulations are consistent with the hypothesis that in the normal lung the whole acinus acts functionally as a gas exchange unit and ventilation-perfusion inequality has an interacinar bais.

Photoelectron branching ratios and asymmetry parameters for the two outermost molecular orbitals of hydrogen cyanide

Triply differential photoelectron spectroscopy has been performed on hydrogen cyanide in the photon energy range 14.5 to 24 eV, using synchrotron radiation. Photoelectron branching ratios and asymmetry parameters are presented for the two outermost molecular orbitals. The vibrationally resolved branching ratio X2 Pi (v3=1)/(v3=0) exhibits strong non-Franck-Condon behaviour from threshold to approximately 19 eV. The results are discussed in relation to similar studies on the isoelectronic molecules, N2, CO and C2H2. The evidence suggests that the prominent non-Franck-Condon feature observed in the HCN+ X2 Pi channel may arise, at least in part, from a shape resonantly enhanced autoionising state converging to a higher ionisation potential.

Photoelectron branching ratios and asymmetry parameters of the two outermost molecular orbitals of methyl cyanide

Vibrationally resolved photoelectron branching ratios and asymmetry parameters have been determined for the two outermost molecular orbitals of methyl cyanide. The results are discussed briefly within the context of similar studies on cyanogen and hydrogen cyanide, and in relation to structures exhibited in the photoionization efficiency curve.