In Silico Design of Heterogeneous Microvascular Trees Using Generative Adversarial Networks and Constrained Constructive Optimization.

OBJECTIVE: Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes in vivo. METHODS: We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension-oriented constrained constructive optimization (LFDO-CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO-CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues. RESULTS: The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity. CONCLUSIONS: These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology.

Pulsatility damping in the microcirculation: Basic pattern and modulating factors.

Blood flow pulsatility is an important determinant of macro- and microvascular physiology. Pulsatility is damped largely in the microcirculation, but the characteristics of this damping and the factors that regulate it have not been fully elucidated yet. Applying computational approaches to real microvascular network geometry, we examined the pattern of pulsatility damping and the role of potential damping factors, including pulse frequency, vascular viscous resistance, vascular compliance, viscoelastic behavior of the vessel wall, and wave propagation and reflection. To this end, three full rat mesenteric vascular networks were reconstructed from intravital microscopic recordings, a one-dimensional (1D) model was used to reproduce pulsatile properties within the network, and potential damping factors were examined by sensitivity analysis. Results demonstrate that blood flow pulsatility is predominantly damped at the arteriolar side and remains at a low level at the venular side. Damping was sensitive to pulse frequency, vascular viscous resistance and vascular compliance, whereas viscoelasticity of the vessel wall or wave propagation and reflection contributed little to pulsatility damping. The present results contribute to our understanding of mechanical forces and their regulation in the microcirculation.

Coalescent angiogenesis-evidence for a novel concept of vascular network maturation.

Angiogenesis describes the formation of new blood vessels from pre-existing vascular structures. While the most studied mode of angiogenesis is vascular sprouting, specific conditions or organs favor intussusception, i.e., the division or splitting of an existing vessel, as preferential mode of new vessel formation. In the present study, sustained (33-h) intravital microscopy of the vasculature in the chick chorioallantoic membrane (CAM) led to the hypothesis of a novel non-sprouting mode for vessel generation, which we termed "coalescent angiogenesis." In this process, preferential flow pathways evolve from isotropic capillary meshes enclosing tissue islands. These preferential flow pathways progressively enlarge by coalescence of capillaries and elimination of internal tissue pillars, in a process that is the reverse of intussusception. Concomitantly, less perfused segments regress. In this way, an initially mesh-like capillary network is remodeled into a tree structure, while conserving vascular wall components and maintaining blood flow. Coalescent angiogenesis, thus, describes the remodeling of an initial, hemodynamically inefficient mesh structure, into a hierarchical tree structure that provides efficient convective transport, allowing for the rapid expansion of the vasculature with maintained blood supply and function during development.

Visualizing the spatiotemporal pattern of yolk sac membrane vascular network by enhanced local fractal analysis.

OBJECTIVE: To establish methods for providing a comprehensive and detailed description of the spatial distribution of the vascular networks, and to reveal the spatiotemporal pattern of the yolk sac membrane vascular network during the angiogenic procedure. METHODS: Addressing the limitations in the conventional local fractal analysis, an improved approach, named scanning average local fractal dimension, was proposed. This method was conducted on 6 high-resolution vascular images of the yolk sac membrane for 3 eggs at two stages (E3 and E4) to characterize the spatial distribution of the complexity of the vascular network. RESULTS: With the proposed method, the spatial distribution of the complexity of the yolk sac membrane vascular network was visualized. From E3 to E4, the local fractal dimension increased in 3 eggs, 1.80 ± 0.02 vs. 1.85 ± 0.02, 1.72 ± 0.03 vs. 1.83 ± 0.02, and 1.77 ± 0.03 vs. 1.82 ± 0.02, respectively. The mean local fractal dimension in the most distal area from the embryo proper was the lowest at E3 while the highest at E4. At E3, the most peaks of the local fractal dimension were located in the vein territories and shifted to artery territories at E4. CONCLUSIONS: The spatial distribution of the complexity of the yolk sac membrane vascular network exhibited diverse patterns at different stages. In addition from E3 to E4, the increment of complexity at the intersection areas between arteries and sinus terminalis was with the most advance. This is consistent with the physiologic evidence. The present work provides a potential approach for investigating the spatiotemporal pattern of the angiogenic process.

Gap junctions regulate vessel diameter in chick chorioallantoic membrane vasculature by both tone-dependent and structural mechanisms.

OBJECTIVE: In this study, we examined the impact of gap junction blockade on chick chorioallantoic membrane microvessels. METHODS: Expression of Cx37, Cx40/42, and Cx43 in chick chorioallantoic membrane tissue was studied by PCR, Western blot, and confocal immunofluorescence microscopy. Vessel diameter changes occurring under gap junction blockade with carbenoxolone (175 µmol/L), palmitoleic acid (100 µmol/L), 43 GAP27 (1 mmol/L) were analyzed by intravital microscopy. To analyze vascular tone, chick chorioallantoic membrane vessels were exposed to a vasodilator cocktail consisting of acetylcholine (10 µmol/L), adenosine (100 µmol/L), papaverine (200 µmol/L), and sodium nitroprusside (10 µmol/L). RESULTS: In chick chorioallantoic membrane lysates, Western blot analysis revealed the expression of Cx40 and Cx43. Immunofluorescence in intact chick chorioallantoic membrane vasculature showed only Cx43, limited to arterial vessel walls. Upon gap junction blockade (3 hours) arterial and venous diameters decreased to 0.50 ± 0.03 and 0.36 ± 0.06 (carbenoxolone), 0.72 ± 0.08 and 0.63 ± 0.15 (palmitoleic acid) and 0.77 ± 0.004 and 0.58 ± 0.05 (GAP27), relative to initial values. Initially, diameter decrease was dominated by increasing vascular tone. After 6 hours, however, vessel tone was reduced, suggesting structural network remodeling. CONCLUSIONS: Our findings suggest a major role for connexins in mediating acute and chronic diameter changes in developing vascular networks.

A hybrid discrete-continuum approach for modelling microcirculatory blood flow.

In recent years, biological imaging techniques have advanced significantly and it is now possible to digitally reconstruct microvascular network structures in detail, identifying the smallest capillaries at sub-micron resolution and generating large 3D structural data sets of size >106 vessel segments. However, this relies on ex vivo imaging; corresponding in vivo measures of microvascular structure and flow are limited to larger branching vessels and are not achievable in three dimensions for the smallest vessels. This suggests the use of computational modelling to combine in vivo measures of branching vessel architecture and flows with ex vivo data on complete microvascular structures to predict effective flow and pressures distributions. In this paper, a hybrid discrete-continuum model to predict microcirculatory blood flow based on structural information is developed and compared with existing models for flow and pressure in individual vessels. A continuum-based Darcy model for transport in the capillary bed is coupled via point sources of flux to flows in individual arteriolar vessels, which are described explicitly using Poiseuille's law. The venular drainage is represented as a spatially uniform flow sink. The resulting discrete-continuum framework is parameterized using structural data from the capillary network and compared with a fully discrete flow and pressure solution in three networks derived from observations of the rat mesentery. The discrete-continuum approach is feasible and effective, providing a promising tool for extracting functional transport properties in situations where vascular branching structures are well defined.

Investigation into the diversity in the fractal dimensions of arterioles and venules in a microvascular network - A quantitative analysis.

Fractal dimension is a robust fractal parameter for estimating the morphology of vascular networks. It reflects the property of vascular networks that may vary and thus, differentiate between individual networks and/or identify physiological and pathological conditions. As such, fractal dimension differs also between arteriolar and venular compartments, yet the underlying reason is so far unclear. In order to understand the mechanisms behind these differences, we quantitatively analyzed the impacts of vessel attributes on the fractal dimension. Fractal dimension and vessel attributes given by vessel density (VD), vessel length density (VL), and diameter index (DI=VD/VL) were analyzed in three microvascular networks of the rat mesentery, which were reconstructed from experimental data. The results show that differences in diameter between arterioles and venules are primarily responsible for arterio-venous differences in fractal dimension. Moreover, multiple linear regression analysis demonstrates that the sensitivity of the variation of fractal dimension to vessel length and diameter varies with the type of the vessels. While the change of vessel length contributes 57.8 ±â€¯3.4% to the variation of arteriolar dimension, vessel diameter contributes 63.9 ±â€¯4.8% to the variation of venular dimension. The present study provides an explanation for the different fractal dimension and dimension variation in arteriolar and venular compartments. It highlights the importance of estimating the fractal dimensions of arterioles and venules separately, which will enhance the ability of feature extraction by fractal analysis in physiological and clinical application.

Microvascular hemodynamics: System properties1.

The hemodynamics of the microcirculation reflect system properties of the involved components. The blood itself is a complex suspension of water, small and large molecules and different cell types. Under most conditions, its rheologic properties are dominated by the different behaviour of fluid and cellular compartments. When perfused through small-bore tubes or vessels, the suspension exhibits specific emergent properties. The Fahraeus-effect and the Fahreaeus-Lindqvist-effect result from the interaction of cellular particles with each other and with the vessel wall. Additional phenomena occur in vascular networks due to the uneven distribution of blood cells and blood plasma at divergent microvascular bifurcations. In order to understand microvascular hemodynamics in vivo but also in artificial microfluidic geometries it is thus necessary to recognize the pertinent system properties on the level of the blood, the microvessels and the microvascular networks or perfused structures.

Coronary Microcirculation in Ischemic Heart Disease.

BACKGROUND: Ischemic heart disease has long been considered to be exlusively caused by stenosis or occlusion. However, the coronary microcirculation too may play an important role in ischemic conditions. Also, the crucial role of microvessels in not only regulating blood flow on a local level but also mediating vascular permeability or inflammatory responses has been recognized. OBJECTIVE: To review important physiological and pathophysiological mechanisms of coronary microcirculatory control with focus on heterogeneity of local perfusion, microvascular permeability and inflammation. METHOD: Selective research of the literature. RESULTS: Heterogeneity is a characteristic of microvascular networks and affects structural and functional parameters such as vessel diameter, length, and connection pattern, flow velocity, wall shear stress, and oxygenation. Microvascular networks are optimized to meet the metabolic demand of all tissue compartments. This requires continuous vascular adaptation regulated by local hemodynamic and metabolic stimuli. Compromising this regulation results in functional arterio-venous shunting and tissue areas with either hyperperfusion or hypoxia in close proximity. In ischemia-reperfusion, increased microvascular permeability may aggravate tissue hypoxia by increasing extravascular pressure and seems to contribute to adverse myocardial remodeling. Transendothelial transport mechanisms and deterioration of the endothelial glycocalyx seem to be major contributors to tissue edema. Also in the context of ischemia-reperfusion, an inflammatory response mediated by venular endothelium expressing specific adhesion molecules contributes to tissue injury. However, anti-inflammatory therapies failed in clinical studies and a multi-targeted approach for cardiac protection is required. CONCLUSION: Disturbances of the coronary microcirculation are involved in different pathophysiological aspects of reperfusion injury.

Pulse wave velocity in the microcirculation reflects both vascular compliance and resistance: Insights from computational approaches.

OBJECTIVE: PWV is the speed of pulse wave propagation through the circulatory system. mPWV emerges as a novel indicator of hypertension, yet it remains unclear how different vascular properties affect mPWV. We aim to identify the biomechanical determinants of mPWV. METHODS: A 1D model was used to simulate PWV in a rat mesenteric microvascular network and, for comparison, in a human macrovascular arterial network. Sensitivity analysis was performed to assess the relationship between PWV and vascular compliance and resistance. RESULTS: The 1D model enabled adequate simulation of PWV in both micro- and macrovascular networks. Simulated arterial PWV changed as a function of vascular compliance but not resistance, in that arterial PWV varied at a rate of 0.30 m/s and -6.18 × 10-3  m/s per 10% increase in vascular compliance and resistance, respectively. In contrast, mPWV depended on both vascular compliance and resistance, as it varied at a rate of 2.79 and -2.64 cm/s per 10% increase in the respective parameters. CONCLUSIONS: The present study identifies vascular compliance and resistance in microvascular networks as critical determinants of mPWV. We anticipate that mPWV can be utilized as an effective indicator for the assessment of microvascular biomechanical properties.

Modeling the hematocrit distribution in microcirculatory networks: A quantitative evaluation of a phase separation model.

OBJECTIVE: Theoretical models are essential tools for studying microcirculatory function. Recently, the validity of a well-established phase separation model was questioned and it was claimed that it produces problematically low hematocrit predictions and lack of red cells in small diameter vessels. We conducted a quantitative evaluation of this phase separation model to establish common ground for future research. METHODS: Model predictions were validated against a comprehensive database with measurements from 4 mesenteric networks. A Bayesian data analysis framework was used to integrate measurements and network model simulations into a combined analysis and to model uncertainties related to network boundary conditions as well as phase separation model parameters. The model evaluation was conducted within a cross-validation scheme. RESULTS: Unlike the recently reported results, our analysis demonstrated good correspondence in global characteristics between measurements and predictions. In particular, predicted hematocrits for vessels with small diameters were consistent with measurements. Incorporating phase separation model parameter uncertainties further reduced the hematocrit validation error by 17% and led to the absence of red-cell-free segments. Corresponding model parameters are presented as alternatives to standard parameters. CONCLUSIONS: Consistent with earlier studies, our quantitative model evaluation supports the continued use of the established phase separation model.

Structural Control of Microvessel Diameters: Origins of Metabolic Signals.

Diameters of microvessels undergo continuous structural adaptation in response to hemodynamic and metabolic stimuli. To ensure adequate flow distribution, metabolic responses are needed to increase diameters of vessels feeding poorly perfused regions. Possible modes of metabolic control include release of signaling substances from vessel walls, from the supplied tissue and from red blood cells (RBC). Here, a theoretical model was used to compare the abilities of these metabolic control modes to provide adequate tissue oxygenation, and to generate blood flow velocities in agreement with experimental observations. Structural adaptation of vessel diameters was simulated for an observed mesenteric network structure in the rat with 576 vessel segments. For each mode of metabolic control, resulting distributions of oxygen and deviations between simulated and experimentally observed flow velocities were analyzed. It was found that wall-derived and tissue-derived growth signals released in response to low oxygen levels could ensure adequate oxygen supply, but RBC-derived signals caused inefficient oxygenation. Closest agreement between predicted and observed flow velocities was obtained with wall-derived growth signals proportional to vessel length. Adaptation in response to oxygen-independent release of a metabolic signal substance from vessel walls or the supplied tissue was also shown to be effective for ensuring tissue oxygenation due to a dilution effect if growth signal substances are released into the blood. The present results suggest that metabolic signals responsible for structural adaptation of microvessel diameters are derived from vessel walls or from perivascular tissue.

Modeling of pulsatile flow-dependent nitric oxide regulation in a realistic microvascular network.

Hemodynamic pulsatility has been reported to regulate microcirculatory function. To quantitatively assess the impact of flow pulsatility on the microvasculature, a mathematical model was first developed to simulate the regulation of NO production by pulsatile flow in the microcirculation. Shear stress and pressure pulsatility were selected as regulators of endothelial NO production and NO-dependent vessel dilation as feedback to control microvascular hemodynamics. The model was then applied to a real microvascular network of the rat mesentery consisting of 546 microvessels. As compared to steady flow conditions, pulsatile flow increased the average NO concentration in arterioles from 256.8±93.1nM to 274.8±101.1nM (P<0.001), with a corresponding increase in vessel dilation by approximately 7% from 27.5±10.6% to 29.4±11.4% (P<0.001). In contrast, NO concentration and vessel size showed a far lesser increase (about 1.7%) in venules under pulsatile flow as compared to steady flow conditions. Network perfusion and flow heterogeneity were improved under pulsatile flow conditions, and vasodilation within the network was more sensitive to heart rate changes than pulse pressure amplitude. The proposed model simulates the role of flow pulsatility in the regulation of a complex microvascular network in terms of NO concentration and hemodynamics under varied physiological conditions.

Dynamic remodeling of arteriolar collaterals after acute occlusion in chick chorioallantoic membrane.

OBJECTIVE: After arteriolar occlusion, collaterals enlarge and initially elevated WSS normalizes. While most previous studies focused on endpoints of such adaptive changes in larger collaterals, the present investigation aimed to continuously determine the relation between WSS and diameter in microvascular collaterals during adaptive reactions. METHODS: In Hamburger-Hamilton stage 40 CAMs, junction points between arteriolar segments were identified and the third upstream segment on one side was occluded. Intravital microscopy recordings were taken for 24 hours post-occlusion. Segment diameter and blood velocity were measured: WSS and capillary density were calculated. RESULTS: After occlusion, vascular diameters exhibited an immediate decrease, then increased with a time constant of 2.5 ± 0.8 hours and reached a plateau of up to 60% above baseline after about 7 hours. Vascular tone showed no significant change. WSS exhibited an immediate increase post-occlusion and linearly returned to baseline after about 12 hours. Local WSS change and diameter change rate showed similar patterns during the initial but not the later phase of post-occlusive adaptation. CONCLUSIONS: CAM collaterals undergo fast structural remodeling within 24 hours post-occlusion. This remodeling might be driven by local WSS and by other regulators within the vascular network.

Coronary microcirculatory pathophysiology: can we afford it to remain a black box?

Coronary microvascular networks play the key role in determining blood flow distribution in the heart. Matching local blood supply to tissue metabolic demand entails continuous adaptation of coronary vessels via regulation of smooth muscle tone and structural dilated vessel diameter. The importance of coronary microcirculation for relevant pathological conditions including angina in patients with normal or near-normal coronary angiograms [microvascular angina (MVA)] and heart failure with preserved ejection fraction (HFpEF) is increasingly recognized. For MVA, clinical studies have shown a prevalence of up to 40% in patients with suspected coronary artery disease and a relevant impact on adverse cardiovascular events including cardiac death, stroke, and heart failure. Despite a continuously increasing number of corresponding clinical studies, the knowledge on pathophysiological cause-effect relations involving coronary microcirculation is, however, still very limited. A number of pathophysiological hypotheses for MVA and HFpEF have been suggested but are not established to a degree, which would allow definition of nosological entities, stratification of affected patients, or development of effective therapeutic strategies. This may be related to a steep decline in experimental (animal) pathophysiological studies in this area during the last 15 years. Since technology to experimentally investigate microvascular pathophysiology in the beating heart is increasingly, in principle, available, a concerted effort to build 'coronary microcirculatory observatories' to close this gap and to accelerate clinical progress in this area is suggested.

Model-based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach.

OBJECTIVE: In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. METHODS: We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. RESULTS: We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than 500 unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. CONCLUSION: Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large data sets acquired as part of microvascular imaging studies.