Toward a multiscale description of microvascular flow regulation: o(2)-dependent release of ATP from human erythrocytes and the distribution of ATP in capillary networks

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

Evidence for role of capillaries in regulation of skeletal muscle oxygen supply

How oxygen (O₂ ) supply to capillaries is regulated to match the tissue's demand is unknown. Erythrocytes have been proposed as sensors in this regulatory mechanism since they release ATP, a vasodilator, in an oxygen saturation (SO₂ )-dependent manner. ATP causes hyperpolarization of endothelial cells resulting in conducted vasodilation to arterioles.

OBJECTIVE

We propose individual capillary units can regulate their own O₂ supply by direct communication to upstream arterioles via electrically coupled endothelium.

METHODS

To test this hypothesis, we developed a transparent micro-exchange device for localized O₂ exchange with surface capillaries of intact tissue. The device was fabricated with an O₂ permeable micro-outlet 0.2 × 1.0 mm. Experiments were performed on rat extensor digitorum longus (EDL) muscle using dual wavelength video microscopy to measure capillary hemodynamics and erythrocyte SO₂ . Responses to local O₂ perturbations were measured with only capillaries positioned over the micro-outlet.

RESULTS

Step changes in the gas mixture %O₂ caused physiological changes in erythrocyte SO₂ , and appropriate changes in flow to offset the O₂ challenge if at least 3-4 capillaries were stimulated.

CONCLUSION

These results support our hypothesis that individual capillary units play a role in regulating their erythrocyte supply in response to a changing O₂ environment.

A two-compartment model of oxygen transport in skeletal muscle using continuously distributed capillaries

For future application to studying regulation of microvascular oxygen delivery, a model is developed for O₂ transport within an idealized volume of tissue, that is perfused by a continuous distribution of capillaries. Considering oxygen diffusion, convection, and consumption, an O₂-dependent transfer term between the capillaries and tissue is used to extend previous single-compartment approaches to include separate tissue and capillary compartments. The coupled tissue-capillary PDE system is considered for unidirectional capillary flow in z, as a simplified model of O₂ transport in skeletal muscle, and steady-state 2D solutions are obtained using boundary conditions in x that are consistent with two experimental situations of interest. To validate the continuous capillary model, comparisons are made of an exact nonlinear solution (for no flux at x=0) to results of an established discrete capillary model (solved via finite differences) for varying capillary density, O₂ consumption rate, and red blood cell velocity. In addition, comparisons of an approximate linearized solution (for fixed PO₂ at x=0) are made to the corresponding discrete capillary solution. Results of the continuous capillary model are presented for varying inlet O₂ saturation, showing the utility of the new model for studying physiological problems. Numerical solution of the new model for problems with time dependence and complex geometry is expected to be substantially more efficient than for the corresponding discrete capillary problems.

Steady-State Tissue Oxygen Distributions Calculated by a Green's Function Method and a Finite Difference Method: A Comparison

Simulations that are meant to determine the steady-state distribution of a diffusible solute such as oxygen in tissues have typically used finite difference methods to solve the diffusion equation. Finite difference methods require a tissue mesh with enough points to resolve oxygen gradients near and between discrete blood vessels. The large number of points that are typically required can make these calculations very slow. In this paper, we investigate a numerical method known as the Green's function method which is not bound by the same constraint. The Green's function method is expected to yield an accurate oxygen distribution more quickly by requiring fewer mesh points. Both methods were applied to calculate the steady state oxygen distribution in a model simulation region. When the Green's function calculation used meshes with 1/2, 1/4 and, 1/8 of the resolution required for the finite-difference mesh, there was good agreement with the finite difference calculation in all cases. When the volume of the domain was increased 8-fold the Green's function method was able to calculate the O₂ field in 22 minutes, whereas the finite difference calculation is expected to take approximately 1 week. The number of steps required for the Green's function calculation increases quadratically with the number of points in the tissue mesh. As a result, small meshes are calculated very quickly using Green's functions, while for larger mesh sizes this method experiences a significant decrease in efficiency.

Overview of mathematical modeling of myocardial blood flow regulation

The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.

Integrative model of coronary flow in anatomically based vasculature under myogenic, shear, and metabolic regulation

Coronary blood flow is regulated to match the oxygen demand of myocytes in the heart wall. Flow regulation is essential to meet the wide range of cardiac workload. The blood flows through a complex coronary vasculature of elastic vessels having nonlinear wall properties, under transmural heterogeneous myocardial extravascular loading. To date, there is no fully integrative flow analysis that incorporates global and local passive and flow control determinants. Here, we provide an integrative model of coronary flow regulation that considers the realistic asymmetric morphology of the coronary network, the dynamic myocardial loading on the vessels embedded in it, and the combined effects of local myogenic effect, local shear regulation, and conducted metabolic control driven by venous O₂ saturation level. The model predicts autoregulation (approximately constant flow over a wide range of coronary perfusion pressures), reduced heterogeneity of regulated flow, and presence of flow reserve, in agreement with experimental observations. Furthermore, the model shows that the metabolic and myogenic regulations play a primary role, whereas shear has a secondary one. Regulation was found to have a significant effect on the flow except under extreme (high and low) inlet pressures and metabolic demand. Novel outcomes of the model are that cyclic myocardial loading on coronary vessels enhances the coronary flow reserve except under low inlet perfusion pressure, increases the pressure range of effective autoregulation, and reduces the network flow in the absence of metabolic regulation. Collectively, these findings demonstrate the utility of the present biophysical model, which can be used to unravel the underlying mechanisms of coronary physiopathology.

Possible roles for ATP release from RBCs exclude the cAMP-mediated Panx1 pathway

Red blood cell (RBC)-derived adenosine triphosphate (ATP) has been proposed as an integral component in the regulation of oxygen supply to skeletal muscle. In ex vivo settings RBCs have been shown to release ATP in response to a number of stimuli, including stimulation of adrenergic receptors. Further evidence suggested that ATP release from RBCs was dependent on activation of adenylate cyclase (AC)/cyclic adenosine monophosphate (cAMP)-dependent pathways and involved the pannexin 1 (Panx1) channel. Here we show that RBCs express Panx1 and confirm its absence in Panx1 knockout (^-/-) RBCs. However, Panx1^-/- mice lack any decrease in exercise performance, challenging the assumptions that Panx1 plays an essential role in increased blood perfusion to exercising skeletal muscle and therefore in ATP release from RBCs. We therefore tested the role of Panx1 in ATP release from RBCs ex vivo in RBC suspensions. We found that stimulation with hypotonic potassium gluconate buffer resulted in a significant increase in ATP in the supernatant, but this was highly correlated with RBC lysis. Next, we treated RBCs with a stable cAMP analog, which did not induce ATP release from wild-type or Panx1^-/- mice. Similarly, multiple pharmacological treatments activating AC in RBCs increased intracellular cAMP levels (as measured via mass spectrometry) but did not induce ATP release. The data presented here question the importance of Panx1 for exercise performance and dispute the general assumption that ATP release from RBCs via Panx1 is regulated via cAMP.

New insights on the regulation of the adenine nucleotide pool of erythrocytes in mouse models

The observation that induced torpor in non-hibernating mammals could result from an increased AMP concentration in circulation led our investigation to reveal that the added AMP altered oxygen transport of erythrocytes. To further study the effect of AMP in regulation of erythrocyte function and systemic metabolism, we generated mouse models deficient in key erythrocyte enzymes in AMP metabolism. We have previously reported altered erythrocyte adenine nucleotide levels corresponding to altered oxygen saturation in mice deficient in both CD73 and AMPD3. Here we further investigate how these Ampd3^-/-/Cd73^-/- mice respond to the administered dose of AMP in comparison with the control models of single enzyme deficiency and wild type. We found that Ampd3^-/-/Cd73^-/- mice are more sensitive to AMP-induced hypometabolism than mice with a single enzyme deficiency, which are more sensitive than wild type. A dose-dependent rightward shift of erythrocyte p50 values in response to increasing amounts of extracellular AMP was observed. We provide further evidence for the direct uptake of AMP by erythrocytes that is insensitive to dipyridamole, a blocker for ENT1. The uptake of AMP by the erythrocytes remained linear at the highest concentration tested, 10mM. We also observed competitive inhibition of AMP uptake by ATP and ADP but not by the other nucleotides and metabolites tested. Importantly, our studies suggest that AMP uptake is associated with an erythrocyte ATP release that is partially sensitive to inhibition by TRO19622 and Ca⁺⁺ ion. Taken together, our study suggests a novel mechanism by which erythrocytes recycle and maintain their adenine nucleotide pool through AMP uptake and ATP release.

Role of erythrocyte-released ATP in the regulation of microvascular oxygen supply in skeletal muscle

In a 1914 book entitled The Respiratory Function of the Blood, Joseph Barcroft stated that 'the cell takes what it needs and leaves the rest'. He postulated that there must be both a 'call for oxygen' and a 'mechanism by which the call elicits a response...' In the past century, intensive investigation has provided significant insights into the haemodynamic and biophysical mechanisms involved in supplying oxygen to skeletal muscle. However, the identification of the mechanism by which tissue oxygen needs are sensed and the affector responsible for altering the upstream vasculature to enable the need to be appropriately met has been a challenge. In 1995, Ellsworth et al. proposed that the oxygen-carrying erythrocyte, by virtue of its capacity to release the vasoactive mediator ATP in response to a decrease in oxygen saturation, could serve both roles. Several in vitro and in situ studies have established that exposure of erythrocytes to reduced oxygen tension induces the release of ATP which does result in a conducted arteriolar vasodilation with a sufficiently rapid time course to make the mechanism physiologically relevant. The components of the signalling pathway for the controlled release of ATP from erythrocytes in response to exposure to low oxygen tension have been determined. In addition, the implications of defective ATP release on human pathological conditions have been explored. This review provides a perspective on oxygen supply and the role that such a mechanism plays in meeting the oxygen needs of skeletal muscle.

Red cell physiology and signaling relevant to the critical care setting

PURPOSE OF REVIEW

Oxygen (O2) delivery, the maintenance of which is fundamental to supporting those with critical illness, is a function of blood O2 content and flow. Here, we review red blood cell (RBC) physiology relevant to disordered O2 delivery in the critically ill.

RECENT FINDINGS

Flow (rather than content) is the focus of O2 delivery regulation. O2 content is relatively fixed, whereas flow fluctuates by several orders of magnitude. Thus, blood flow volume and distribution vary to maintain coupling between O2 delivery and demand. The trapping, processing and delivery of nitric oxide (NO) by RBCs has emerged as a conserved mechanism through which regional blood flow is linked to biochemical cues of perfusion sufficiency. We will review conventional RBC physiology that influences O2 delivery (O2 affinity & rheology) and introduce a new paradigm for O2 delivery homeostasis based on coordinated gas transport and vascular signaling by RBCs.

SUMMARY

By coordinating vascular signaling in a fashion that links O2 and NO flux, RBCs couple vessel caliber (and thus blood flow) to O2 need in tissue. Malfunction of this signaling system is implicated in a wide array of pathophysiologies and may be explanatory for the dysoxia frequently encountered in the critical care setting.

Identification of signalling cascades involved in red blood cell shrinkage and vesiculation

Even though red blood cell (RBC) vesiculation is a well-documented phenomenon, notably in the context of RBC aging and blood transfusion, the exact signalling pathways and kinases involved in this process remain largely unknown. We have established a screening method for RBC vesicle shedding using the Ca²⁺ ionophore ionomycin which is a rapid and efficient method to promote vesiculation. In order to identify novel pathways stimulating vesiculation in RBC, we screened two libraries: the Library of Pharmacologically Active Compounds (LOPAC) and the Selleckchem Kinase Inhibitor Library for their effects on RBC from healthy donors. We investigated compounds triggering vesiculation and compounds inhibiting vesiculation induced by ionomycin. We identified 12 LOPAC compounds, nine kinase inhibitors and one kinase activator which induced RBC shrinkage and vesiculation. Thus, we discovered several novel pathways involved in vesiculation including G protein-coupled receptor (GPCR) signalling, the phosphoinositide 3-kinase (PI3K)–Akt (protein kinase B) pathway, the Jak–STAT (Janus kinase–signal transducer and activator of transcription) pathway and the Raf–MEK (mitogen-activated protein kinase kinase)–ERK (extracellular signal-regulated kinase) pathway. Moreover, we demonstrated a link between casein kinase 2 (CK2) and RBC shrinkage via regulation of the Gardos channel activity. In addition, our data showed that inhibition of several kinases with unknown functions in mature RBC, including Alk (anaplastic lymphoma kinase) kinase and vascular endothelial growth factor receptor 2 (VEGFR-2), induced RBC shrinkage and vesiculation.

After screening two libraries of small bioactive molecules and kinase inhibitors, we identified several signalling pathways to be involved in red blood cell (RBC) shrinkage and vesiculation. These include the Jak (Janus kinase)–STAT (signal transducer and activator of transcription) pathway, phosphoinositide 3-kinase (PI3K)–Akt pathway, the Raf–MEK (mitogen-activated protein kinase kinase)–ERK (extracellular signal-regulated kinase) pathway and GPCR (G protein-coupled receptor) signalling.

A computational model of a microfluidic device to measure the dynamics of oxygen-dependent ATP release from erythrocytes

Erythrocytes are proposed to be involved in blood flow regulation through both shear- and oxygen-dependent mechanisms for the release of adenosine triphosphate (ATP), a potent vasodilator. In a recent study, the dynamics of shear-dependent ATP release from erythrocytes was measured using a microfluidic device with a constriction in the channel to increase shear stress. The brief period of increased shear stress resulted in ATP release within 25 to 75 milliseconds downstream of the constriction. The long-term goal of our research is to apply a similar approach to determine the dynamics of oxygen-dependent ATP release. In the place of the constriction, an oxygen permeable membrane would be used to decrease the hemoglobin oxygen saturation of erythrocytes flowing through the channel. This paper describes the first stage in achieving that goal, the development of a computational model of the proposed experimental system to determine the feasibility of altering oxygen saturation rapidly enough to measure ATP release dynamics. The computational model was constructed based on hemodynamics, molecular transport of oxygen and ATP, kinetics of luciferin/luciferase reaction for reporting ATP concentrations, light absorption by hemoglobin, and sensor characteristics. A linear model of oxygen saturation-dependent ATP release with variable time delay was used in this study. The computational results demonstrate that a microfluidic device with a 100 µm deep channel will cause a rapid decrease in oxygen saturation over the oxygen permeable membrane that yields a measurable light intensity profile for a change in rate of ATP release from erythrocytes on a timescale as short as 25 milliseconds. The simulation also demonstrates that the complex dynamics of ATP release from erythrocytes combined with the consumption by luciferin/luciferase in a flowing system results in light intensity values that do not simply correlate with ATP concentrations. A computational model is required for proper interpretation of experimental data.

Synergistic effects of C-peptide and insulin on low O2-induced ATP release from human erythrocytes

Erythrocytes participate in the matching of oxygen (O2) delivery with local need in skeletal muscle via the release of O2 and the vasodilator, ATP. It was reported that a concentration of insulin found in humans with insulin resistance inhibits low O2-induced ATP release. However, in vivo, insulin is coreleased with connecting peptide (C-peptide) at equimolar concentrations, but because of the shorter insulin half-life, the peptides circulate at ratios of C-peptide to insulin ranging from 1:1 to 6:1. Here, we investigate the hypothesis that C-peptide and insulin work synergistically to maintain low O2-induced ATP release from human erythrocytes. Using a thin-film tonometer to alter O2 tension, we determined that either C-peptide or insulin alone inhibits low O2-induced ATP release in a concentration-dependent manner; however, coadministration of the peptides at a 1:1 ratio does not (n = 5; P < 0.05). Because this ratio of C-peptide to insulin is not present in vivo for extended periods, we also investigated the effect of additional physiological ratios on ATP release. In the presence of insulin concentrations that would be found in fasting humans (0.05 nM), C-peptide to insulin ratios of 4:1 and 6:1 did not adversely affect low O2-induced ATP release. However, at a concentration of insulin found in the peripheral circulation of humans under postprandial conditions (0.5 nM), a ratio of C-peptide to insulin of 6:1 inhibited low O2-induced ATP release (n = 5). These findings demonstrate a heretofore unrecognized synergism between C-peptide and insulin that could have physiological importance in the regulation of perfusion distribution in skeletal muscle.

Modeling steady state SO2-dependent changes in capillary ATP concentration using novel O2 micro-delivery methods

Adenosine triphosphate (ATP) is known to be released from the erythrocyte in an oxygen (O2) dependent manner. Since ATP is a potent vasodilator, it is proposed to be a key regulator in the pathway that mediates micro-vascular response to varying tissue O2 demand. We propose that ATP signaling mainly originates in the capillaries due to the relatively long erythrocyte transit times in the capillary and the short ATP diffusion distance to the electrically coupled endothelium. We have developed a computational model to investigate the effect of delivering or removing O2 to limited areas at the surface of a tissue with an idealized parallel capillary array on total ATP concentration. Simulations were conducted when exposing full surface to perturbations in tissue O2 tension (PO2) or locally using a circular micro-outlet (~100 μm in diameter), a square micro-slit (200 × 200 μm), or a rectangular micro-slit (1000 μm wide × 200 μm long). Results indicated the rectangular micro-slit has the optimal dimensions for altering hemoglobin saturations (SO2) in sufficient number capillaries to generate effective changes in total [ATP]. This suggests a threshold for the minimum number of capillaries that need to be stimulated in vivo by imposed tissue hypoxia to induce a conducted micro-vascular response. SO2 and corresponding [ATP] changes were also modeled in a terminal arteriole (9 μm in diameter) that replaces 4 surface capillaries in the idealized network geometry. Based on the results, the contribution of terminal arterioles to the net change in [ATP] in the micro-vascular network is minimal although they would participate as O2 sources thus influencing the O2 distribution. The modeling data presented here provide important insights into designing a novel micro-delivery device for studying micro-vascular O2 regulation in the capillaries in vivo.

Blunted temporal activity of microvascular perfusion heterogeneity in metabolic syndrome: a new attractor for peripheral vascular disease?

A key clinical outcome for peripheral vascular disease (PVD) in patients is a progressive decay in skeletal muscle performance and its ability to resist fatigue with elevated metabolic demand. We have demonstrated that PVD in obese Zucker rats (OZR) is partially due to increased perfusion distribution heterogeneity at successive microvascular bifurcations within skeletal muscle. As this increased heterogeneity (γ) is longitudinally present in the network, its cumulative impact is a more heterogeneous distribution of perfusion between terminal arterioles than normal, causing greater regional tissue ischemia. To minimize this negative outcome, a likely compensatory mechanism against an increased γ should be an increased temporal switching at arteriolar bifurcations to minimize downstream perfusion deficits. Using in situ cremaster muscle, we determined that temporal activity (the cumulative sum of absolute differences between successive values of γ, taken every 20 s) was lower in OZR than in control animals, and this difference was present in both proximal (1A-2A) and distal (3A-4A) arteriolar bifurcations. Although adrenoreceptor blockade (phentolamine) improved temporal activity in 1A-2A arteriolar bifurcations in OZR, this was without impact in the distal microcirculation, where only interventions against oxidant stress (Tempol) and thromboxane A(2) activity (SQ-29548) were effective. Analysis of the attractor for γ indicated that it was not only elevated in OZR but also exhibited severe reductions in range, suggesting that the ability of the microcirculation to respond to any challenge is highly restricted and may represent the major contributor to the manifestation of poor muscle performance at this age in OZR.