Integrative Modeling of Small Artery Structure and Function Uncovers Critical Parameters for Diameter Regulation

Organ perfusion is regulated by vasoactivity and structural adaptation of small arteries and arterioles. These resistance vessels are sensitive to pressure, flow and a range of vasoactive stimuli. Several strongly interacting control loops exist. As an example, the myogenic response to a change of pressure influences the endothelial shear stress, thereby altering the contribution of shear-dependent dilation to the vascular tone. In addition, acute responses change the stimulus for structural adaptation and vice versa. Such control loops are able to maintain resistance vessels in a functional and stable state, characterized by regulated wall stress, shear stress, matched active and passive biomechanics and presence of vascular reserve. In this modeling study, four adaptation processes are identified that together with biomechanical properties effectuate such integrated regulation: control of tone, smooth muscle cell length adaptation, eutrophic matrix rearrangement and trophic responses. Their combined action maintains arteries in their optimal state, ready to cope with new challenges, allowing continuous long-term vasoregulation. The exclusion of any of these processes results in a poorly regulated state and in some cases instability of vascular structure.     

Structural response of microcirculatory networks to changes in demand: information transfer by shear stress

Matching blood flow to metabolic demand in terminal vascular beds involves coordinated changes in diameters of vessels along flow pathways, requiring upstream and downstream transfer of information on local conditions. Here, the role of information transfer mechanisms in structural adaptation of microvascular networks after a small change in capillary oxygen demand was studied using a theoretical model. The model includes diameter adaptation and information transfer via vascular reactions to wall shear stress, transmural pressure, and oxygen levels. Information transfer is additionally effected by conduction along vessel walls and by convection of metabolites. The model permits selective blocking of information transfer mechanisms. Six networks, based on in vivo data, were considered. With information transfer, increases in network conductance and capillary oxygen supply were amplified by factors of 4.9 +/- 0.2 and 9.4 +/- 1.1 (means +/- SE), relative to increases when information transfer was blocked. Information transfer by flow coupling alone, in which increased shear stress triggers vascular enlargement, gave amplifications of 4.0 +/- 0.3 and 4.9 +/- 0.5. Other information transfer mechanisms acting alone gave amplifications below 1.6. Thus shear-stress-mediated flow coupling is the main mechanism for the structural adjustment of feeding and draining vessel diameters to small changes in capillary oxygen demand.     

Structural adaptation of microvascular networks: functional roles of adaptive responses

Terminal vascular beds continually adapt to changing demands. A theoretical model is used to simulate structural diameter changes in response to hemodynamic and metabolic stimuli in microvascular networks. Increased wall shear stress and decreased intravascular pressure are assumed to stimulate diameter increase. Intravascular partial pressure of oxygen (PO(2)) is estimated for each segment. Decreasing PO(2) is assumed to generate a metabolic stimulus for diameter increase, which acts locally, upstream via conduction along vessel walls, and downstream via metabolite convection. By adjusting the sensitivities to these stimuli, good agreement is achieved between predicted network characteristics and experimental data from microvascular networks in rat mesentery. Reduced pressure sensitivity leads to increased capillary pressure with reduced viscous energy dissipation and little change in tissue oxygenation. Dissipation decreases strongly with decreased metabolic response. Below a threshold level of metabolic response flow shifts to shorter pathways through the network, and oxygen supply efficiency decreases sharply. In summary, the distribution of vessel diameters generated by the simulated adaptive process allows the network to meet the functional demands of tissue while avoiding excessive viscous energy dissipation.     

Structural Adaptation and Heterogeneity of Normal and Tumor Microvascular Networks

Relative to normal tissues, tumor microcirculation exhibits high structural and functional heterogeneity leading to hypoxic regions and impairing treatment efficacy. Here, computational simulations of blood vessel structural adaptation are used to explore the hypothesis that abnormal adaptive responses to local hemodynamic and metabolic stimuli contribute to aberrant morphological and hemodynamic characteristics of tumor microcirculation. Topology, vascular diameter, length, and red blood cell velocity of normal mesenteric and tumor vascular networks were recorded by intravital microscopy. Computational models were used to estimate hemodynamics and oxygen distribution and to simulate vascular diameter adaptation in response to hemodynamic, metabolic and conducted stimuli. The assumed sensitivity to hemodynamic and conducted signals, the vascular growth tendency, and the random variability of vascular responses were altered to simulate ‘normal’ and ‘tumor’ adaptation modes. The heterogeneous properties of vascular networks were characterized by diameter mismatch at vascular branch points (d³_var) and deficit of oxygen delivery relative to demand (O_2def). In the tumor, d³_var and O_2def were higher (0.404 and 0.182) than in normal networks (0.278 and 0.099). Simulated remodeling of the tumor network with ‘normal’ parameters gave low values (0.288 and 0.099). Conversely, normal networks attained tumor-like characteristics (0.41 and 0.179) upon adaptation with ‘tumor’ parameters, including low conducted sensitivity, increased growth tendency, and elevated random biological variability. It is concluded that the deviant properties of tumor microcirculation may result largely from defective structural adaptation, including strongly reduced responses to conducted stimuli.     

Exercise training-induced coronary vascular adaptation.

Aerobic exercise training induces an increase in coronary vascular transport capacity. This increased transport capacity is the result of increases in both blood flow capacity and capillary exchange capacity. These functional changes are the result of two major types of adaptive responses, structural vascular adaptation and altered control of vascular resistance. Structural vascular adaptation occurs in response to exercise training in at least two forms, increases in the cross-sectional area of the proximal coronary arteries and angiogenesis. Angiogenesis has been demonstrated in that training causes moderate cardiac hypertrophy while maintaining or increasing capillary density and increasing arteriolar density. Training-induced changes in coronary vascular control have been shown to include altered coronary responses to vasoactive substances, changes in endothelium-mediated vasoregulation, and alterations in the cellular-molecular control of intracellular free Ca2+ in both endothelial and vascular smooth muscle cells isolated from coronary arteries of exercise-trained animals. The signal or signals for these adaptive responses remain unknown. The hypothesis that the adaptive strategy entails maintenance of normal shear stress in coronary arterial vessels is discussed. We propose that as a result of training-induced structural vascular adaptations and alterations in the control of vascular resistance, shear stress throughout the coronary vasculature is returned to the level present in sedentary animals. The signal for adaptation may be peak shear stress during exercise and/or average shear stress over a 24-h period of time.     

Molecular basis of the effects of shear stress on vascular endothelial cells

Blood vessels are constantly exposed to hemodynamic forces in the form of cyclic stretch and shear stress due to the pulsatile nature of blood pressure and flow. Endothelial cells (ECs) are subjected to the shear stress resulting from blood flow and are able to convert mechanical stimuli into intracellular signals that affect cellular functions, e.g., proliferation, apoptosis, migration, permeability, and remodeling, as well as gene expression. The ECs use multiple sensing mechanisms to detect changes in mechanical forces, leading to the activation of signaling networks. The cytoskeleton provides a structural framework for the EC to transmit mechanical forces between its luminal, abluminal and junctional surfaces and its interior, including the cytoplasm, the nucleus, and focal adhesion sites. Endothelial cells also respond differently to different modes of shear forces, e.g., laminar, disturbed, or oscillatory flows. In vitro studies on cultured ECs in flow channels have been conducted to investigate the molecular mechanisms by which cells convert the mechanical input into biochemical events, which eventually lead to functional responses. The knowledge gained on mechano-transduction, with verifications under in vivo conditions, will advance our understanding of the physiological and pathological processes in vascular remodeling and adaptation in health and disease.     

Theoretical model of metabolic blood flow regulation: roles of ATP release by red blood cells and conducted responses

A proposed mechanism for metabolic flow regulation involves the saturation-dependent release of ATP by red blood cells, which triggers an upstream conducted response signal and arteriolar vasodilation. To analyze this mechanism, a theoretical model is used to simulate the variation of oxygen and ATP levels along a flow pathway of seven representative segments, including two vasoactive arteriolar segments. The conducted response signal is defined by integrating the ATP concentration along the vascular pathway, assuming exponential decay of the signal in the upstream direction with a length constant of approximately 1 cm. Arteriolar tone depends on the conducted metabolic signal and on local wall shear stress and wall tension. Arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model predicts that conducted responses stimulated by ATP release in venules and propagated to arterioles can account for increases in perfusion in response to increased oxygen demand that are consistent with experimental findings at low to moderate oxygen consumption rates. Myogenic and shear-dependent responses are found to act in opposition to this mechanism of metabolic flow regulation.     

Theoretical comparison of wall-derived and erythrocyte-derived mechanisms for metabolic flow regulation in heterogeneous microvascular networks

The objective of this study is to compare the effectiveness of metabolic signals derived from erythrocytes and derived from the vessel wall for regulating blood flow in heterogeneous microvascular networks. A theoretical model is used to simulate blood flow, mass transport, and vascular responses. The model accounts for myogenic, shear-dependent, and metabolic flow regulation. Metabolic signals are assumed to be propagated upstream along vessel walls via a conducted response. Arteriolar tone is assumed to depend on the conducted metabolic signal as well as local wall shear stress and wall tension, and arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model shows that under certain conditions metabolic regulation based on wall-derived signals can be more effective in matching perfusion to local oxygen demand relative to regulation based on erythrocyte-derived signals, resulting in higher extraction and lower oxygen deficit. The lower effectiveness of the erythrocyte-derived signal is shown to result in part from the unequal partition of hematocrit at diverging bifurcations, such that low-flow vessels tend to receive a reduced hematocrit and thereby experience a reduced erythrocyte-derived metabolic signal. The model simulations predict that metabolic signals independent of erythrocytes may play an important role in local metabolic regulation of vascular tone and flow distribution in heterogeneous microvessel networks.     

Regulation of endothelial connexin40 expression by shear stress

Endothelial connexin (Cx)40 plays an important role in signal propagation along blood vessel walls, modulating vessel diameter and thereby blood flow. Blood flow, in turn, has been shown to alter endothelial Cx40 expression. However, the timing and shear stress dependence of this relationship have remained unclear, as have the signal transduction pathways involved and the functional implications. Therefore, the aim of this study was to quantify the effects of shear stress on endothelial Cx40 expression, to analyze the role of phosphoinositide 3-kinase (PI3K)/Akt signaling involved, and to assess the possible functional consequences for the adaptation of microvascular networks. First-passage human umbilical vein endothelial cells were exposed to defined shear stress conditions and analyzed for Cx40 using real-time RT-PCR and immunoblot analysis. Shear stress caused long-term induction of Cx40 protein expression, with two short-term mRNA peaks at 4 and 16 h, indicating the dynamic nature of the adaptation process. Maximum shear stress-dependent induction was observed at shear levels between 6 and 10 dyn/cm(2). Simulation of this pattern of shear-dependent Cx expression in a vascular adaptation model of a microvascular network led to an improved fit for the simulated results to experimental measurements. Cx40 expression was greatly reduced by inhibiting PI3K or Akt, with PI3K activity being required for basal Cx40 expression and Akt activity taking part in its shear stress-dependent induction.     

Mechanotransduction and endothelial cell homeostasis: the wisdom of the cell

Vascular endothelial cells (ECs) play significant roles in regulating circulatory functions. Mechanical stimuli, including the stretch and shear stress resulting from circulatory pressure and flow, modulate EC functions by activating mechanosensors, signaling pathways, and gene and protein expressions. Mechanical forces with a clear direction (e.g., the pulsatile shear stress and the uniaxial circumferential stretch existing in the straight part of the arterial tree) cause only transient molecular signaling of pro-inflammatory and proliferative pathways, which become downregulated when such directed mechanical forces are sustained. In contrast, mechanical forces without a definitive direction (e.g., disturbed flow and relatively undirected stretch seen at branch points and other regions of complex geometry) cause sustained molecular signaling of pro-inflammatory and proliferative pathways. The EC responses to directed mechanical stimuli involve the remodeling of EC structure to minimize alterations in intracellular stress/strain and elicit adaptive changes in EC signaling in the face of sustained stimuli; these cellular events constitute a feedback control mechanism to maintain vascular homeostasis and are atheroprotective. Such a feedback mechanism does not operate effectively in regions of complex geometry, where the mechanical stimuli do not have clear directions, thus placing these areas at risk for atherogenesis. The mechanotransduction-induced EC adaptive processes in the straight part of the aorta represent a case of the "Wisdom of the Cell," as a part of the more general concept of the "Wisdom of the Body" promulgated by Cannon, to maintain cellular homeostasis in the face of external perturbations.     

Roles of fluid shear stress in physiological regulation of vascular structure and function

The effects of fluid shear stress on the function and structure of the vascular system are outlined, based on the findings obtained in our laboratory or of our colleagues. First, it is pointed out that the adaptive response of the vascular wall to flow changes which we observed in the canine carotid artery shunted with the jugular vein altering the internal diameter to keep the wall shear stress constant, can attain the optimum vascular branching structure as predicted in the minimum work model by Murray. Electronmicroscopic studies of similarly shunted arteries revealing various morphological changes in the endothelial cells have suggested that the shear stress initially affects the endothelium. The in vitro experiments using cultured endothelial cells as well have exhibited that the mitotic activity of the cells significantly increases by applying fluid shear stress. From these findings, it is concluded that the adaptive response of the endothelium to the fluid shear stress is an inherent and key process locally regulating the vascular system to be in the most functional state.     

Dynamic Endothelial Cell Rearrangements Drive Developmental Vessel Regression

Patterning of functional blood vessel networks is achieved by pruning of superfluous connections. The cellular and molecular principles of vessel regression are poorly understood. Here we show that regression is mediated by dynamic and polarized migration of endothelial cells, representing anastomosis in reverse. Establishing and analyzing the first axial polarity map of all endothelial cells in a remodeling vascular network, we propose that balanced movement of cells maintains the primitive plexus under low shear conditions in a metastable dynamic state. We predict that flow-induced polarized migration of endothelial cells breaks symmetry and leads to stabilization of high flow/shear segments and regression of adjacent low flow/shear segments.     

A potential role of smooth muscle tone in early hypertension: a theoretical study

A conspicuous long-term consequence of hypertension is a thickening of the arterial wall, which many suggest returns the circumferential wall stress toward its normal value. This thickening results from an increase in smooth muscle and extracellular matrix, with the associated growth and remodeling processes depending on a host of regulatory signals that likely include the altered mechanical environment. Although the precise mechanotransduction pathways remain unknown, we propose that vasoconstriction may be an early response of the arterial wall to a step-change in pressure. In particular, computations suggest that such a response can decrease the magnitude and transmural gradients of the pressure-induced wall stresses and return the mean wall shear stress toward its homeostatic value. Such an initial 'compensatory vasoconstriction' could also help set into motion subsequent growth and remodeling responses due to growth regulatory characteristics of the vasoactive molecules (e.g., nitric oxide, endothelin-1, angiotensin-II). Although the consequences of growth and remodeling have been the focus of prior biomechanical and histological studies, early responses dictate subsequent developments and therefore deserve increased attention in vascular biomechanics and mechanobiology.     

Stability of Metabolic Correlations under Changing Environmental Conditions in Escherichia coli – A Systems Approach

Background

Biological systems adapt to changing environments by reorganizing their cellular and physiological program with metabolites representing one important response level. Different stresses lead to both conserved and specific responses on the metabolite level which should be reflected in the underlying metabolic network.

Methodology/Principal Findings

Starting from experimental data obtained by a GC-MS based high-throughput metabolic profiling technology we here develop an approach that: (1) extracts network representations from metabolic condition-dependent data by using pairwise correlations, (2) determines the sets of stable and condition-dependent correlations based on a combination of statistical significance and homogeneity tests, and (3) can identify metabolites related to the stress response, which goes beyond simple observations about the changes of metabolic concentrations. The approach was tested with Escherichia coli as a model organism observed under four different environmental stress conditions (cold stress, heat stress, oxidative stress, lactose diauxie) and control unperturbed conditions. By constructing the stable network component, which displays a scale free topology and small-world characteristics, we demonstrated that: (1) metabolite hubs in this reconstructed correlation networks are significantly enriched for those contained in biochemical networks such as EcoCyc, (2) particular components of the stable network are enriched for functionally related biochemical pathways, and (3) independently of the response scale, based on their importance in the reorganization of the correlation network a set of metabolites can be identified which represent hypothetical candidates for adjusting to a stress-specific response.

Conclusions/Significance

Network-based tools allowed the identification of stress-dependent and general metabolic correlation networks. This correlation-network-based approach does not rely on major changes in concentration to identify metabolites important for stress adaptation, but rather on the changes in network properties with respect to metabolites. This should represent a useful complementary technique in addition to more classical approaches.     

A mechanism for arteriolar remodeling based on maintenance of smooth muscle cell activation

Structural adaptation in arterioles is part of normal vascular physiology but is also seen in disease states such as hypertension. Smooth muscle cell (SMC) activation has been shown to be central to microvascular remodeling. We hypothesize that, in a remodeling process driven by SMC activation, stress sensitivity of the vascular wall is a key element in the process of achieving a stable vascular structure. We address whether the adaptive changes in arterioles under different conditions can arise through a common mechanism: remodeling in a stress-sensitive wall driven by a shift in SMC activation. We present a simple dynamic model and show that structural remodeling of the vessel radius by rearrangement of the wall material around a lumen of a different diameter and driven by differences in SMC activation can lead to vascular structures similar to those observed experimentally under various conditions. The change in structure simultaneously leads to uniform levels of circumferential wall stress and wall strain, despite differences in transmural pressure. A simulated vasoconstriction caused by increased SMC activation leads to inward remodeling, whereas outward remodeling follows relaxation of the vascular wall. The results are independent of the specific myogenic properties of the vessel. The simulated results are robust in the face of parameter changes and, hence, may be generalized to vessels from different vascular beds.     

On the influence of variation in haemodynamic conditions on the generation and growth of cerebral aneurysms and atherogenesis: a computational model

A risk-factor criterion, based on near-wall haemodynamic conditions, for the assessment of vascular pathology risk is developed and tested. This criterion has its foundation on experimentally observed vascular wall responses to oscillatory and swirling wall shear stress patterns and is applied to the results of computational simulations. We test this model on two anatomically accurate vascular segments, where pathologies are either commonplace or have already been developed, i.e. a healthy carotid bifurcation and a cerebral fusiform aneurysm. In the case of the former, the risk-assessment criterion predicts the emergence of atherosclerosis of the same locations that the disease is usually encountered. In the case of the latter, the risk factor shows increased probability for the appearance of secondary, “baby”, aneurysms at certain locations.     

Control of endothelial cell gene expression by flow

The vessel wall is constantly subjected to, and affected by, the stresses resulting from the hemodynamic stimuli of transmural pressure and flow. At the interface between blood and the vessel wall, the endothelial cell plays a crucial role in controlling vessel structure and function in response to changes in hemodynamic conditions. Using bovine aortic endothelium monolayers, we show that fluid shear stress causes simultaneous differential regulation of endothelial-derived products. We also report that the downregulation of endothelin-1 mRNA by flow is a reversible process, and through the use of uncharged dextran supplementation demonstrate it to be shear stress-rather than shear rate-dependent. Recent work on the effect of fluid shear stress on endothelial cell gene expression of a number of potent endothelial products is reviewed, including vasoactive substances, autocrine and paracrine growth factors, thrombosis/fibrinolysis modulators, chemotactic factors, surface receptors and immediate-early genes. The encountered patterns of gene expression responses are classified into three categories: a transient increase with return to baseline (type I), a sustained increase (type II) and a biphasic response consisting of an early transient increase of varying extent followed by a pronounced and sustained decrease (type III). The importance of the dynamic character of the flow stimulus and the magnitude dependence of the response are presented. Potential molecular mechanisms of shear-induced gene regulation, including putative shear stress response elements (SSRE), are discussed. These results suggest exquisite modulation of endothelial cell phenotype by local fluid shear stress and may offer insight into the mechanism of flow-dependent vascular remodeling and the observed propensity of atherosclerosis formation around bifurcations and areas of low shear stress.     

Mapping vascular response to in vivo Hemodynamics: application to increased flow at the basilar terminus

Hemodynamic forces play critical roles in vascular pathologies such as atherosclerosis, aneurysms, and stenosis. However, detailed relationships between the specific in vivo hemodynamic microenvironment and vascular responses leading to the triggering or exacerbation of pathological remodeling of the vessel remain elusive. We have developed a hemodynamics-biology co-mapping technique that enables in situ correlation between the in vivo blood flow field and vascular changes secondary to hemodynamic insult. The hemodynamics profile is obtained from computational fluid dynamics simulation within the vascular geometry reconstructed from three-dimensional in vivo images, whereas the vascular response is obtained from histology or immunohistochemistry on harvested vascular tissue. The hemodynamics field is virtually sectioned in the histological slicing planes and digitally co-mapped with the histological images, thereby enabling correlation of the specific local vascular responses with the inciting hemodynamic stresses. We demonstrate application of this technique to rabbit basilar terminus subjected to elevated flow. Morphological changes at the basilar terminus 5 days after the flow increase were co-mapped with the initial wall shear stress and wall shear stress gradient distributions, from which localization of destructive remodeling in a specific hemodynamic zone was noticed. This method paves the way for further investigations to determine the connection between in vivo mechanical stimuli and biological responses, such as initiation of aneurysmal remodeling.     

Isotropy and anisotropy of the arterial wall

The passive biomechanical response of intact cylindrical rat carotid arteries is studied in vitro and compared with the mechanical response of rubber tubes. Using true stress and natural strain in the definition of the incremental modulus of elasticity, the tissue wall properties are analyzed over wide ranges of simultaneous circumferential and longitudinal deformations. The type of loading chosen is 'physiological' i.e. symmetric: the cylindrical segments are subjected to internal pressure and axial prestretch without torsion or shear. Several aspects pertaining to the choice of parameters characterizing the material are discussed and the analysis pertaining to the deformational behavior of a hypothetical compliant tube with Hookean wall material is presented. The experimental results show that while rubber response can be adequately represented as linearly elastic and isotropic, the overall response of vascular tissue is highly non-linear and anisotropic. However, for states of deformation that occur in vivo, the elasticity of arteries is quite similar to that of rubber tubes and as such the arterial wall may be viewed as incrementally isotropic for the range of deformations that occur in vivo.     

Angiogenesis: An Adaptive Dynamic Biological Patterning Problem

Formation of functionally adequate vascular networks by angiogenesis presents a problem in biological patterning. Generated without predetermined spatial patterns, networks must develop hierarchical tree-like structures for efficient convective transport over large distances, combined with dense space-filling meshes for short diffusion distances to every point in the tissue. Moreover, networks must be capable of restructuring in response to changing functional demands without interruption of blood flow. Here, theoretical simulations based on experimental data are used to demonstrate that this patterning problem can be solved through over-abundant stochastic generation of vessels in response to a growth factor generated in hypoxic tissue regions, in parallel with refinement by structural adaptation and pruning. Essential biological mechanisms for generation of adequate and efficient vascular patterns are identified and impairments in vascular properties resulting from defects in these mechanisms are predicted. The results provide a framework for understanding vascular network formation in normal or pathological conditions and for predicting effects of therapies targeting angiogenesis.