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.

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.

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.

Structure and hemodynamics of vascular networks in the chorioallantoic membrane of the chicken.

The chick chorioallantoic membrane (CAM) is extensively used as an in vivo model. Here, structure and hemodynamics of CAM vessel trees were analyzed and compared with predictions of Murray's law. CAM microvascular networks of Hamburger-Hamilton stage 40 chick embryos were scanned by videomicroscopy. Three networks with ∼3,800, 580, and 480 segments were digitally reconstructed, neglecting the capillary mesh. Vessel diameters (D) and segment lengths were measured, and generation numbers and junctional exponents at bifurcations were derived. In selected vessels, flow velocities (v) and hematocrit were measured. Hemodynamic simulations, incorporating the branching of capillaries from preterminal vessels, were used to estimate v, volume flow, shear stress (τ), and pressure for all segments of the largest network. For individual arteriovenous flow pathways, terminal arterial and venous generation numbers are negatively correlated, leading to low variability of total topological and morphological pathway lengths. Arteriolar velocity is proportional to diameter (v∝D1.03 measured, v∝D0.93 modeling), giving nearly uniform τ levels (τ∝D0.05). Venular trees exhibit slightly higher exponents (v∝D1.3, τ∝D0.38). Junctional exponents at divergent and convergent bifurcations were 2.05 ± 1.13 and 1.97 ± 0.95 (mean ± SD) in contrast to the value 3 predicted by Murray's law. In accordance with Murray's law, τ levels are (nearly) maintained in CAM arterial (venular) trees, suggesting vascular adaptation to shear stress. Arterial and venous trees show an interdigitating arrangement providing homogeneous flow pathway properties and have preterminal capillary branches. These properties may facilitate efficient oxygen exchange in the CAM during rapid embryonic growth.

Metabolic control of microvascular networks: oxygen sensing and beyond.

The metabolic regulation of blood flow is central to guaranteeing an adequate supply of blood to the tissues and microvascular network stability. It is assumed that vascular reactions to local oxygenation match blood supply to tissue demand via negative-feedback regulation. Low oxygen (O2) levels evoke vasodilatation, and thus an increase of blood flow and oxygen supply, by increasing (decreasing) the release of vasodilatory (vasoconstricting) metabolic signal substances with decreasing partial pressure of O2. This review analyses the principles of metabolic vascular control with a focus on the prevailing feedback regulations. We propose the following hypotheses with respect to vessel diameter adaptation. (1) In addition to O2-dependent signaling, metabolic vascular regulation can be effected by signal substances produced independently of local oxygenation (reflecting the presence of cells) due to the dilution effect. (2) Control of resting vessel tone, and thus perfusion reserve, could be explained by a vascular activity/hypoxia memory. (3) Vasodilator but not vasoconstrictor signaling can prevent shunt perfusion via signal conduction upstream to feeding arterioles. (4) For low perfusion heterogeneity in the steady state, metabolic signaling from the vessel wall or a perivascular tissue sleeve is optimal. (5) For amplification of perfusion during transient increases of tissue demand, red blood cell-derived vasodilators or vasoconstrictors diluted in flowing blood may be relevant.

A one-dimensional mathematical model for studying the pulsatile flow in microvascular networks.

Techniques that model microvascular hemodynamics have been developed for decades. While the physiological significance of pressure pulsatility is acknowledged, most of the microcirculatory models use steady flow approaches. To theoretically study the extent and transmission of pulsatility in microcirculation, dynamic models need to be developed. In this paper, we present a one-dimensional model to describe the dynamic behavior of microvascular blood flow. The model is applied to a microvascular network from a rat mesentery. Intravital microscopy was used to record the morphology and flow velocities in individual vessel segments, and boundaries are defined according to the experimental data. The system of governing equations constituting the model is solved numerically using the discontinuous Galerkin method. An implicit integration scheme is adopted to increase computing efficiency. The model allows the simulation of the dynamic properties of blood flow in microcirculatory networks, including the pressure pulsatility (quantified by a pulsatility index) and pulse wave velocity (PWV). From the main input arteriole to the main output venule, the pulsatility index decreases by 66.7%. PWV obtained along arterioles declines with decreasing diameters, with mean values of 77.16, 25.31, and 8.30 cm/s for diameters of 26.84, 17.46, and 13.33 µm, respectively. These results suggest that the 1D model developed is able to simulate the characteristics of pressure pulsatility and wave propagation in complex microvascular networks.

Structural adaptation of microvessel diameters in response to metabolic stimuli: where are the oxygen sensors?

Maintenance of functional vascular networks requires structural adaptation of vessel diameters in response to hemodynamic and metabolic conditions. The mechanisms by which diameters respond to the metabolic state are not known, but may involve the release of vasoactive substances in response to low oxygen by tissue ("tissue signaling", e.g., CO2, adenosine), by vessel walls ("wall signaling", e.g., prostaglandins, adenosine), and/or by red blood cells (RBCs) ("RBC signaling", e.g., ATP and nitric oxide). Here, the goal was to test the potential of each of these locations of oxygen-dependent signaling to control steady-state vascular diameters and tissue oxygenation. A previously developed theoretical model of structural diameter adaptation based on experimental data on microvascular network morphology and hemodynamics was used. Resulting network characteristics were analyzed with regard to tissue oxygenation (Oxdef; percentage of tissue volume with PO2<1 Torr) and the difference between estimated blood flow velocities and corresponding experimental data [velocity error (Verr); root mean square deviation of estimated vs. measured velocity]. Wall signaling led to Oxdef<1% and to the closest hemodynamic similarity (Verr: 0.60). Tissue signaling also resulted in a low oxygen deficit, but a higher Verr (0.73) and systematic diameter deviations. RBC signaling led to widespread hypoxia (Oxdef: 4.7%), unrealistic velocity distributions (Verr: 0.81), and shrinkage of small vessels. The results suggest that wall signaling plays a central role in structural control of vessel diameters in microvascular networks of given angioarchitecture. Tissue-derived and RBC-derived signaling of oxygen levels may be more relevant for the regulation of angiogenesis and/or smooth muscle tone.

Chronic kidney disease induces a systemic microangiopathy, tissue hypoxia and dysfunctional angiogenesis.

Chronic kidney disease (CKD) is associated with excessive mortality from cardiovascular disease (CVD). Endothelial dysfunction, an early manifestation of CVD, is consistently observed in CKD patients and might be linked to structural defects of the microcirculation including microvascular rarefaction. However, patterns of microvascular rarefaction in CKD and their relation to functional deficits in perfusion and oxygen delivery are currently unknown. In this in-vivo microscopy study of the cremaster muscle microcirculation in BALB/c mice with moderate to severe uremia, we show in two experimental models (adenine feeding or subtotal nephrectomy), that serum urea levels associate incrementally with a distinct microangiopathy. Structural changes were characterized by a heterogeneous pattern of focal microvascular rarefaction with loss of coherent microvascular networks resulting in large avascular areas. Corresponding microvascular dysfunction was evident by significantly diminished blood flow velocity, vascular tone, and oxygen uptake. Microvascular rarefaction in the cremaster muscle paralleled rarefaction in the myocardium, which was accompanied by a decrease in transcription levels not only of the transcriptional regulator HIF-1α, but also of its target genes Angpt-2, TIE-1 and TIE-2, Flkt-1 and MMP-9, indicating an impaired hypoxia-driven angiogenesis. Thus, experimental uremia in mice associates with systemic microvascular disease with rarefaction, tissue hypoxia and dysfunctional angiogenesis.

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.

Measuring blood flow velocity from intravital video recordings.

There is an obvious scientific interest in computing blood flow velocity from intravital microscopy using digital video cameras attached to microscopes. Therefore, software capable of measuring blood flow velocity from videos is of major importance. In this work, a novel software tool is presented. The software tackles three main issues in velocity measurement from videos, the registration, segmentation, and finally the measuring itself. The software was tested in chick chorioallantoic membrane (CAM) videos captured with different resolutions, frame rates, and even cameras. The obtained results show the robustness achieved.

Simulation of microcirculatory hemodynamics: estimation of boundary condition using particle swarm optimization.

Estimation of the boundary condition is a critical problem in simulating hemodynamics in microvascular networks. This paper proposed a boundary estimation strategy based on a particle swarm optimization (PSO) algorithm, which aims to minimize the number of vessels with inverted flow direction in comparison to the experimental observation. The algorithm took boundary values as the particle swarm and updated the position of the particles iteratively to approach the optimization target. The method was tested in a real rat mesenteric network. With random initial boundary values, the method achieved a minimized 9 segments with an inverted flow direction in the network with 546 vessels. Compared with reported literature, the current work has the advantage of a better fit with experimental observations and is more suitable for the boundary estimation problem in pulsatile hemodynamic models due to the experiment-based optimization target selection.

Modeling of angioadaptation: insights for vascular development.

Vascular beds are generated by vasculogenesis and sprouting angiogenesis, and these processes have strong stochastic components. As a result, vascular patterns exhibit significant heterogeneity with respect to the topological arrangement of the individual vessel segments and the characteristics (length, number of segments) of different arterio-venous pathways. This structural heterogeneity tends to cause heterogeneous distributions of flow and oxygen availability in tissue. However, these quantities must be maintained within tolerable ranges to allow normal tissue function. This is achieved largely through adjustment of vascular flow resistance by control of vessel diameters. While short-term diameter control by changes in vascular tone in arterioles and small arteries plays an important role, in the long term an even more important role is played by structural adaptation (angioadaptation), occurring in response to metabolic and hemodynamic signals. The effectiveness, stability and robustness of this angioadaptation depend sensitively on the nature and strength of the vascular responses involved and their interactions with the network structure. Mathematical models are helpful in understanding these complex interactions, and can be used to simulate the consequences of failures in sensing or signal transmission mechanisms. For the tumor microcirculation, this strategy of combining experimental observations with theoretical models, has led to the hypothesis that dysfunctional information transport via vascular connexins is a major cause of the observed vascular pathology and increased heterogeneity in oxygen distribution.

Remodeling of blood vessels: responses of diameter and wall thickness to hemodynamic and metabolic stimuli.

Vascular functions, including tissue perfusion and peripheral resistance, reflect continuous structural adaptation (remodeling) of blood vessels in response to several stimuli. Here, a theoretical model is presented that relates the structural and functional properties of microvascular networks to the adaptive responses of individual segments to hemodynamic and metabolic stimuli. All vessels are assumed to respond, according to a common set of adaptation rules, to changes in wall shear stress, circumferential wall stress, and tissue metabolic status (indicated by partial pressure of oxygen). An increase in vessel diameter with increasing wall shear stress and an increase in wall mass with increased circumferential stress are needed to ensure stable vascular adaptation. The model allows quantitative predictions of the effects of changes in systemic hemodynamic conditions or local adaptation characteristics on vessel structure and on peripheral resistance. Predicted effects of driving pressure on the ratio of wall thickness to vessel diameter are consistent with experimental observations. In addition, peripheral resistance increases by approximately 65% for an increase in driving pressure from 50 to 150 mm Hg. Peripheral resistance is predicted to be markedly increased in response to a decrease in vascular sensitivity to wall shear stress, and to be decreased in response to increased tissue metabolic demand. This theoretical approach provides a framework for integrating available information on structural remodeling in the vascular system and predicting responses to changing conditions or altered vascular reactivity, as may occur in hypertension.