Emergence of matched airway and vascular trees from fractal rules

The bronchial, arterial, and venous trees of the lung are complex interwoven structures. Their geometries are created during fetal development through common processes of branching morphogenesis. Insights from fractal geometry suggest that these extensively arborizing trees may be created through simple recursive rules. Mathematical models of Turing have demonstrated how only a few proteins could interact to direct this branching morphogenesis. Development of the airway and vascular trees could, therefore, be considered an example of emergent behavior as complex structures are created from the interaction of only a few processes. However, unlike inanimate emergent structures, the geometries of the airway and vascular trees are highly stereotyped. This review will integrate the concepts of emergence, fractals, and evolution to demonstrate how the complex branching geometries of the airway and vascular trees are ideally suited for gas exchange in the lung. The review will also speculate on how the heterogeneity of blood flow and ventilation created by the vascular and airway trees is overcome through their coordinated construction during fetal development.     

Engineered blood and lymphatic capillaries in 3-D VEGF-fibrin-collagen matrices with interstitial flow

In vitro endothelial cell organization into capillaries is a long standing challenge of tissue engineering. We recently showed the utility of low level interstitial flow in guiding the organization of endothelial cells through a 3-D fibrin matrix-containing covalently bound vascular endothelial growth factor (VEGF). Here this synergistic phenomenon was extended to explore the effects of matrix composition on in vitro capillary morphogenesis of human blood versus lymphatic endothelial cells (BECs and LECs). Different mixtures of fibrin and collagen were used in conjunction with constant concentrations of matrix-bound VEGF and slow interstitial flow over 10 days. Interestingly, the BECs and LECs each showed a distinct preference in terms of organization for matrix composition: LECs organized the most extensively in a fibrin-only matrix, while BEC organization was optimized in the compliant collagen-containing matrices. Furthermore, the BECs and LECs produced architecturally different structures; while BECs organized in thick, branched networks containing wide lumen, the LECs were elongated into slender, overlapping networks with fine lumen. These data demonstrate the importance of the 3-D matrix composition in facilitating and coordinating BEC and LEC capillary morphogenesis, which is important for in vitro vascularization of engineered tissues.     

Autocrine EGF receptor activation mediates endothelial cell migration and vascular morphogenesis induced by VEGF under interstitial flow

We show here that autocrine ligand activation of epidermal growth factor (EGF) receptor in combination with interstitial flow is critically involved in the morphogenetic response of endothelial cells to VEGF stimulation. Human umbilical vein endothelial cell (HUVEC) monolayers cultured on a collagen gel and exposed to low interstitial flow in the absence of EGF and VEGF remained viable and mitotic but exhibited little evidence of vascular morphogenesis. Addition of VEGF produced a flow-dependent morphogenetic response within 48 to 72 h, characterized by branched capillary-like structures. The response was substantially abolished by inhibitors related to the autocrine EGF receptor pathway including Galardin, AG1478, PD98059, and an EGF receptor-blocking antibody, indicating that regulation of the morphogenetic process operates via autocrine EGF receptor activation. Moreover, we observed that in our system the EGF receptor was always activated independently of the interstitial flow, and, in addition, the EGF receptor inhibitors used above reduced the phosphorylation state of the receptor, correlating with inhibition of capillary morphogenesis. Finally, 5'bromo-2'-deoxyuridine (BrdU) labeling identified dividing cells at the monolayer but not in the extending capillary-like structures. EGF pathway inhibitors Galardin and AG1478 did not reduce BrdU incorporation in the monolayer, indicating that the EGF-receptor-mediated morphogenetic behavior is mainly due to cell migration rather than proliferation. Based on these results, we propose a two-step model for in vitro capillary morphogenesis in response to VEGF stimulation with interstitial fluid flow: monolayer maintenance by mitotic activity independent of EGF receptors and a migratory response mediated by autocrine EGF receptor activation wherein cells establish capillary-like structures.     

Blood vascular architecture of the rat lingual papillae with special reference to their relations to the connective tissue papillae and surface structures: a light and scanning electron microscope study

Subepithelial blood vessels of the rat lingual papillae and their spatial relations to the connective tissue papillae and surface structures were demonstrated by light and scanning electron microscopy. In the rat, four types of papillae were distinguished on the dorsal surface of the tongue, i.e. the filiform, fungiform, foliate and circumvallate papillae. Vascular beds of various appearance were found in all four types of lingual papillae: a simple or twisted capillary loop in the filiform papilla; a basket- or petal-like network in the fungiform papilla; a ring-like network in the foliate papilla, and a conglomerated network surrounded by double heart-shaped capillary networks in the circumvallate papilla. These characteristic vascular beds corresponded to the shape of the connective tissue papillae and surface structures. The vascular bed beneath the gustatory epithelium in the fungiform, foliate and circumvallate papilla consisted of fine capillary networks next to the taste buds.     

The Stiffness of Three-dimensional Ionic Self-assembling Peptide Gels Affects the Extent of Capillary-like Network Formation

Improving our ability to control capillary morphogenesis has implications for not only better understanding of basic biology, but also for applications in tissue engineering and in vitro testing. Numerous biomaterials have been investigated as cellular supports for these applications and the biophysical environment biomaterials provide to cells has been increasingly recognized as an important factor in directing cell function. Here, the ability of ionic self-assembling peptide gels to support capillary morphogenesis and the effect of their mechanical properties is investigated. When placed in a physiological salt solution, these oligopeptides spontaneously self-assemble into gels with an extracellular matrix (ECM)-like microarchitecture. To evaluate the ability of three-dimensional (3D) self-assembled peptide gels to support capillary-like network formation, human umbilical vein endothelial cells (HUVECs) were embedded within RAD16-I ((RADA)₄) or RAD16-II ((RARADADA)₂) peptide gels with various stiffness values. As peptide stiffness is decreased cells show increased elongation and are increasingly able to contract gels. The observation that capillary morphogenesis is favored in more malleable substrates is consistent with previous reports using natural biomaterials. The structural properties of peptide gels and their ability to support capillary morphogenesis in vitro make them promising biomaterials to investigate for numerous biomedical applications.     

Homeobox B3 promotes capillary morphogenesis and angiogenesis

Endothelial cells (EC) express several members of the Homeobox (Hox) gene family, suggesting a role for these morphoregulatory mediators during angiogenesis. We have previously established that Hox D3 is required for expression of integrin alphavbeta3 and urokinase plasminogen activator (uPA), which contribute to EC adhesion, invasion, and migration during angiogenesis. We now report that the paralogous gene, Hox B3, influences angiogenic behavior in a manner that is distinct from Hox D3. Antisense against Hox B3 impaired capillary morphogenesis of dermal microvascular EC cultured on basement membrane extracellular matrices. Although levels of Hox D3-dependent genes were maintained in these cells, levels of the ephrin A1 ligand were markedly attenuated. Capillary morphogenesis could be restored, however, by addition of recombinant ephrin A1/Fc fusion proteins. To test the impact of Hox B3 on angiogenesis in vivo, we constitutively expressed Hox B3 in the chick chorioallantoic membrane using avian retroviruses that resulted in an increase in vascular density and angiogenesis. Thus, while Hox D3 promotes the invasive or migratory behavior of EC, Hox B3 is required for the subsequent capillary morphogenesis of these new vascular sprouts and, together, these results support the hypothesis that paralogous Hox genes perform complementary functions within a particular tissue type.     

Construction of Multi-Scale Consistent Brain Networks: Methods and Applications

Mapping human brain networks provides a basis for studying brain function and dysfunction, and thus has gained significant interest in recent years. However, modeling human brain networks still faces several challenges including constructing networks at multiple spatial scales and finding common corresponding networks across individuals. As a consequence, many previous methods were designed for a single resolution or scale of brain network, though the brain networks are multi-scale in nature. To address this problem, this paper presents a novel approach to constructing multi-scale common structural brain networks from DTI data via an improved multi-scale spectral clustering applied on our recently developed and validated DICCCOLs (Dense Individualized and Common Connectivity-based Cortical Landmarks). Since the DICCCOL landmarks possess intrinsic structural correspondences across individuals and populations, we employed the multi-scale spectral clustering algorithm to group the DICCCOL landmarks and their connections into sub-networks, meanwhile preserving the intrinsically-established correspondences across multiple scales. Experimental results demonstrated that the proposed method can generate multi-scale consistent and common structural brain networks across subjects, and its reproducibility has been verified by multiple independent datasets. As an application, these multi-scale networks were used to guide the clustering of multi-scale fiber bundles and to compare the fiber integrity in schizophrenia and healthy controls. In general, our methods offer a novel and effective framework for brain network modeling and tract-based analysis of DTI data.     

A class of flow bifurcation models with lognormal distribution and fractal dispersion

We report a quantitative analysis of a simple dichotomous branching tree model for blood flow in vascular networks. Using the method of moment-generating function and geometric Brownian motion from stochastic mathematics, our analysis shows that a vascular network with asymmetric branching and random variation at each bifurcating point gives rise to an asymptotic lognormal flow distribution with a positive skewness. The model exhibits a fractal scaling in the dispersion of the regional flow in the branches. Experimentally measurable fractal dimension of the relative dispersion in regional flow is analytically calculated in terms of the asymmetry and the variance at local bifurcation; hence the model suggests a powerful method to obtain the physiological information on local flow bifurcation in terms of flow dispersion analysis. Both the fractal behavior and the lognormal distribution are intimately related to the fact that it is the logarithm of flow, rather than flow itself, which is the natural variable in the tree models. The kinetics of tracer washout is also discussed in terms of the lognormal distribution.     

Role of Src in angiopoietin 1-induced capillary morphogenesis of endothelial cells: Effect of chronic hypoxia on Src inhibition by PP2

Signal transduction pathways leading to angiopoietin 1 (Ang1)-induced capillary morphogenesis by endothelial cells remain poorly defined. Angiogenic cellular responses by endothelial cells may be modulated in vivo by chronic hypoxia, such as that induced by tumors. Here, we studied Ang1-induced capillary morphogenesis in human umbilical-vein endothelial cells (HUVECs) cultured chronically under normoxic (21% oxygen) or hypoxic (1.5% oxygen) conditions. Downregulation of Src using a small interfering RNA (siRNA) inhibited Ang1-induced capillary morphogenesis of HUVECs cultured under both conditions by blocking cell spreading and protrusion. Ang1 upregulated the Src-dependent secretion of vascular endothelial growth factor-A (VEGF-A). Blockade of endogenous VEGF-A also inhibited Ang1-induced capillary morphogenesis. Addition of exogenous VEGF-A restored cell spreading and protrusion, leading to Ang1-induced capillary morphogenesis of Src siRNA-treated HUVECs, suggesting that Ang1-induced VEGF-A secretion through Src was required for capillary morphogenesis. PP2 inhibited both Ang1-induced capillary morphogenesis and Src activation in HUVECs cultured under normoxic conditions, but the PP2 activity was significantly impaired in HUVECs cultured under hypoxic conditions. Expression of multidrug resistance-associated protein 1 (MRP 1) was upregulated in hypoxic HUVECs, and treatment with MRP 1 siRNA restored the inhibitory action of PP2. Taken together, our results suggest that Ang1 induces capillary morphogenesis in HUVECs through Src-dependent upregulation of endogenous VEGF-A. Conditions of chronic hypoxia impaired the effect of PP2, possibly via MRP 1.     

Pattern formation during vasculogenesis

Vasculogenesis, the assembly of the first vascular network, is an intriguing developmental process that yields the first functional organ system of the embryo. In addition to being a fundamental part of embryonic development, vasculogenic processes also have medical importance. To explain the organizational principles behind vascular patterning, we must understand how morphogenesis of tissue level structures can be controlled through cell behavior patterns that, in turn, are determined by biochemical signal transduction processes. Mathematical analyses and computer simulations can help conceptualize how to bridge organizational levels and thus help in evaluating hypotheses regarding the formation of vascular networks. Here, we discuss the ideas that have been proposed to explain the formation of the first vascular pattern: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and sprouting guided by cell–cell contacts. Birth Defects Research (Part C) 96:153–162, 2012. © 2012 Wiley Periodicals, Inc.     

Angiogenic morphogenesis driven by dynamic and heterogeneous collective endothelial cell movement

Angiogenesis is a complex process, which is accomplished by reiteration of modules such as sprouting, elongation and bifurcation, that configures branching vascular networks. However, details of the individual and collective behaviors of vascular endothelial cells (ECs) during angiogenic morphogenesis remain largely unknown. Herein, we established a time-lapse imaging and computer-assisted analysis system that quantitatively characterizes behaviors in sprouting angiogenesis. Surprisingly, ECs moved backwards and forwards, overtaking each other even at the tip, showing an unknown mode of collective cell movement with dynamic 'cell-mixing'. Mosaic analysis, which enabled us to monitor the behavior of individual cells in a multicellular structure, confirmed the 'cell-mixing' phenomenon of ECs that occurs at the whole-cell level. Furthermore, an in vivo EC-tracking analysis revealed evidence of cell-mixing and overtaking at the tip in developing murine retinal vessels. In parametrical analysis, VEGF enhanced tip cell behavior and directed EC migration at the stalk during branch elongation. These movements were counter-regulated by EC-EC interplay via γ-secretase-dependent Dll4-Notch signaling, and might be promoted by EC-mural cell interplay. Finally, multiple regression analysis showed that these molecule-mediated tip cell behaviors and directed EC migration contributed to effective branch elongation. Taken together, our findings provide new insights into the individual and collective EC movements driving angiogenic morphogenesis. The methodology used for this analysis might serve to bridge the gap in our understanding between individual cell behavior and branching morphogenesis.     

In vitro formation of capillary networks using optical lithographic techniques

Tissue engineering approaches have been developed for vascular grafts, but success has been limited to arterial replacements of large-caliber vessels. We have developed an innovative technique to transplant engineered capillary networks by printing techniques. Endothelial cells were cultured on a patterned substrate, in which network patterns were generated by prior optical lithography. Subsequently, the patterned cells were transferred to extracellular matrix and tissue at which point they changed their morphologies and formed tubular structures. Microinjection of dye showed that the micrometer-scale tubular structure had in vitro flow potential. When capillary-like networks engineered on amnion membranes were transplanted into mice, we found blood cells inside of the lumen of the transplanted capillary-like structure. This is the first report of the in vitro formation of capillary networks using cell transfer technique, and this novel technique may open the way for development of rapid and effective blood perfusion systems in regenerative medicine.     

VEGF regulates cell behavior during vasculogenesis

Prominent among molecules that control neovascular processes is vascular endothelial growth factor (VEGF). The VEGF ligands comprise a family of well-studied mitogens/permeability factors that bind cell surface receptor tyrosine kinases. Targets include VEGF receptor-1/Flt1 and VEGF receptor-2/Flk1. Mice lacking genes for VEGF ligand or VEGF receptor-2 die early in gestation, making it difficult to determine the precise nature of underlying endothelial cellular behavior(s). To examine the effect(s) of VEGF signaling on cell behavior in detail, we conducted loss-of-function studies using avian embryos. Injection of soluble VEGFR-1 results in malformed vascular networks and the absence of large vessels. In the most severe cases embryos exhibited vascular atresia. Closely associated with the altered phenotype was a clear endothelial cell response-a marked decrease in cell protrusive activity. Further, we demonstrate that VEGF gain of function strikingly increased cell protrusive activity. Together, our data show that VEGF/VEGF receptor signaling regulates endothelial cell protrusive activity, a key determinant of blood vessel morphogenesis. We propose that VEGF functions as an instructive molecule during de novo blood vessel morphogenesis.     

Modeling the early stages of vascular network assembly

In vertebrates, networks of capillary vessels supply tissues with nutrients. Capillary patterns are closely mimicked by endothelial cells cultured on basement membrane proteins that allow single randomly dispersed cells to self-organize into vascular networks. Here we provide a model including chemoattraction as the fundamental mechanism for cell-to-cell communication in order to identify key parameters in the complexity of the formation of vascular patterns. By flanking biological experiments, theoretical insights and numerical simulations, we provide strong evidence that endothelial cell number and the range of activity of a chemoattractant factor regulate vascular network formation and size. We propose a mechanism linking the scale of formed endothelial structures to the range of cell-to-cell interaction mediated by the release of chemoattractants.     

Fractal analysis of extra‐embryonic vascularization in Japanese quail embryos exposed to extremely low frequency magnetic fields

Magnetic fields (MF) can alter the dynamic behavior of vascular tissue and may have a stimulatory or inhibitory effect on blood vessel growth. Fractal geometry has been used in several studies as a tool to describe the development of blood vascular networks. Due to its self‐similarity, irregularity, fractional dimension, and dependence on the scale of vessel dimensions, vascular networks can be taken as fractal objects. In this work, we calculated the fractal dimension by the methods of box counting (D_bc) and information dimension (D_inf) to evaluate the development of blood vessels of the yolk sac membrane (YSM) from quail embryos exposed to MF with a magnetic flux density of 1 mT and a frequency of 60 Hz. The obtained results showed that when the MF was applied to embryos aged between 48 and 72 h, in sessions of 2 h (6 h/day) and 3 h (9 h/day) with exposure intervals between 6 and 5 h, respectively, blood vascular formation was inhibited. Exposure sessions shorter than 2 h or longer than 3 h had no observable change on the vascular process. In contrast, the magnetic field had no observable change on the YSM vascular network for embryos aged between 72 and 96 h, irrespective of the exposure time. In conclusion, these results show a “window effect” regarding exposure time. Bioelectromagnetics 34:114–121, 2013. © 2012 Wiley Periodicals, Inc.     

Vascular endothelial cell adherens junction assembly and morphogenesis induced by sphingosine-1-phosphate.

Vascular endothelial cells undergo morphogenesis into capillary networks in response to angiogenic factors. We show here that sphingosine-1-phosphate (SPP), a platelet-derived bioactive lipid, activates the EDG-1 and -3 subtypes of G protein-coupled receptors on endothelial cells to regulate angiogenesis. SPP induces the Gi/mitogen-activated protein kinase/cell survival pathway and the small GTPase Rho- and Raccoupled adherens junction assembly. Both EDG-1-and EDG-3-regulated signaling pathways are required for endothelial cell morphogenesis into capillary-like networks. Indeed, SPP synergized with polypeptide angiogenic growth factors in the formation of mature neovessels in vivo. These data define SPP as a novel regulator of angiogenesis.     

Multifractal analysis of the species structure of freshwater hydrobiocenoses

The principles and methods of fractal analysis of the species structure of freshwater phytoplankton, zooplankton, and macrozoobenthos communities of plain water reservoirs and urban waterbodies are discussed. The theoretical foundation and experimental verification are provided for the authors?? concept of self-similar (quasi-fractal) nature of the species structure of communities. According to this concept, the adequate mathematical image of species richness accumulation with growing sampling effort is quasi-monofractals, while the generalized geometric image of the species structure of the community is a multifractal spectrum.