The influence of radial RBC distribution, blood velocity profiles, and glycocalyx on coupled NO/O2 transport

A model of anemic tissue perfusion after blood transfusion shows critical role of endothelial response to shear stress stimuli

Although some of the cardiovascular responses to changes in hematocrit (Hct) are not fully quantified experimentally, available information is sufficient to build a mathematical model of the consequences of treating anemia by introducing RBCs into the circulation via blood transfusion. We present such a model, which describes how the treatment of normovolemic anemia with blood transfusion impacts oxygen (O₂) delivery (DO₂, the product of blood O₂ content and arterial blood flow) by the microcirculation. Our analysis accounts for the differential response of the endothelium to the wall shear stress (WSS) stimulus, changes in nitric oxide (NO) production due to modification of blood viscosity caused by alterations of both hematocrit (Hct) and cell free layer thickness, as well as for their combined effects on microvascular blood flow and DO₂. Our model shows that transfusions of 1- and 2-unit of blood have a minimal effect on DO₂ if the microcirculation is unresponsive to the WSS stimulus for NO production that causes vasodilatation increasing blood flow and DO₂. Conversely, in a fully WSS responsive organism, blood transfusion significantly enhances blood flow and DO₂, because increased viscosity stimulates endothelial NO production causing vasodilatation. This finding suggests that evaluation of a patients' pretransfusion endothelial WSS responsiveness should be beneficial in determining the optimal transfusion requirements for treating patients with anemia.NEW & NOTEWORTHY Transfusion of 1 or 2 units of blood accounts for about 3/4 of the world blood consumption of 119 million units per year, whereas a current world demand deficit is on the order of 100 million units. Therefore, factors supporting the practice of transfusing 1 unit instead of 2 are of interest, given their potential to expand the number of interventions without increasing blood availability. Our mathematical model provides a physiological support for this practice.

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

Effect of spatial heterogeneity and colocalization of eNOS and capacitative calcium entry channels on shear stress-induced NO production by endothelial cells: A modeling approach

Introduction

Colocalization of endothelial nitric oxide synthase (eNOS) and capacitative Ca²⁺ entry (CCE) channels in microdomains such as cavaeolae in endothelial cells (ECs) has been shown to significantly affect intracellular Ca²⁺ dynamics and NO production, but the effect has not been well quantified.

Methods

We developed a two-dimensional continuum model of an EC integrating shear stress-mediated ATP production, intracellular Ca²⁺ mobilization, and eNOS activation to investigate the effects of spatial colocalization of plasma membrane eNOS and CCE channels on Ca²⁺ dynamics and NO production in response to flow-induced shear stress. Our model examines the hypothesis that subcellular colocalization of cellular components can be critical for optimal coupling of NO production to blood flow.

Results

Our simulations predict that heterogeneity of CCE can result in formation of microdomains with significantly higher Ca²⁺ compared to the average cytosolic Ca²⁺. Ca²⁺ buffers with lower or no mobility further enhanced Ca²⁺ gradients relative to mobile buffers. Colocalization of eNOS to CCE channels significantly increased NO production.

Conclusions

Our results provide quantitative understanding for the role of spatial heterogeneity and the compartmentalization of signals in regulation of shear stress-induced NO production.

A dynamic computational network model for the role of nitric oxide and the myogenic response in microvascular flow regulation

OBJECTIVES

The effect of NO on smooth muscle cell contractility is crucial in regulating vascular tone, blood flow, and O₂ delivery. Quantitative predictions for interactions between the NO production rate and the myogenic response for microcirculatory blood vessels are lacking.

METHODS

We developed a computational model of a branching microcirculatory network with four representative classes of resistance vessels to predict the effect of endothelium-derived NO on the microvascular pressure-flow response. Our model links vessel scale biotransport simulations of NO and O₂ delivery to a mechanistic model of autoregulation and myogenic tone in a simplified microcirculatory network.

RESULTS

The model predicts that smooth muscle cell NO bioavailability significantly contributes to resting vascular tone of resistance vessels. Deficiencies in NO seen during hypoxia or ischemia lead to a decreased vessel diameter for all classes at a given intravascular pressure. At the network level, NO deficiencies lead to an increase in pressure drop across the vessels studied, a downward shift in the pressure-flow curve, and a decrease in the effective range of the autoregulatory response.

CONCLUSIONS

Our model predicts the steady state and transient behavior of resistance vessels to perturbations in blood pressure, including effects of NO bioavailability on vascular regulation.

Nitrite-Mediated Hypoxic Vasodilation Predicted from Mathematical Modeling and Quantified from in Vivo Studies in Rat Mesentery

Nitric oxide (NO) generated from nitrite through nitrite reductase activity in red blood cells has been proposed to play a major role in hypoxic vasodilation. However, we have previously predicted from mathematical modeling that much more NO can be derived from tissue nitrite reductase activity than from red blood cell nitrite reductase activity. Evidence in the literature suggests that tissue nitrite reductase activity is associated with xanthine oxidoreductase (XOR) and/or aldehyde oxidoreductase (AOR). We investigated the role of XOR and AOR in nitrite-mediated vasodilation from computer simulations and from in vivo exteriorized rat mesentery experiments. Vasodilation responses to nitrite in the superfusion medium bathing the mesentery equilibrated with 5% O₂ (normoxia) or zero O₂ (hypoxia) at either normal or acidic pH were quantified. Experiments were also conducted following intraperitoneal (IP) injection of nitrite before and after inhibiting XOR with allopurinol or inhibiting AOR with raloxifene. Computer simulations for NO and O₂ transport using reaction parameters reported in the literature were also conducted to predict nitrite-dependent NO production from XOR and AOR activity as a function of nitrite concentration, PO₂ and pH. Experimentally, the largest arteriolar responses were found with nitrite >10 mM in the superfusate, but no statistically significant differences were found with hypoxic and acidic conditions in the superfusate. Nitrite-mediated vasodilation with IP nitrite injections was reduced or abolished after inhibiting XOR with allopurinol (p < 0.001). Responses to IP nitrite before and after inhibiting AOR with raloxifene were not as consistent. Our mathematical model predicts that under certain conditions, XOR and AOR nitrite reductase activity in tissue can significantly elevate smooth muscle cell NO and can serve as a compensatory pathway when endothelial NO production is limited by hypoxic conditions. Our theoretical and experimental results provide further evidence for a role of tissue nitrite reductases to contribute additional NO to compensate for reduced NO production by endothelial nitric oxide synthase during hypoxia. Our mathematical model demonstrates that under extreme hypoxic conditions with acidic pH, endogenous nitrite levels alone can be sufficient for a functionally significant increase in NO bioavailability. However, these conditions are difficult to achieve experimentally.

Shear-Induced Nitric Oxide Production by Endothelial Cells

We present a biochemical model of the wall shear stress-induced activation of endothelial nitric oxide synthase (eNOS) in an endothelial cell. The model includes three key mechanotransducers: mechanosensing ion channels, integrins, and G protein-coupled receptors. The reaction cascade consists of two interconnected parts. The first is rapid activation of calcium, which results in formation of calcium-calmodulin complexes, followed by recruitment of eNOS from caveolae. The second is phosphorylation of eNOS by protein kinases PKC and AKT. The model also includes a negative feedback loop due to inhibition of calcium influx into the cell by cyclic guanosine monophosphate (cGMP). In this feedback, increased nitric oxide (NO) levels cause an increase in cGMP levels, so that cGMP inhibition of calcium influx can limit NO production. The model was used to predict the dynamics of NO production by an endothelial cell subjected to a step increase of wall shear stress from zero to a finite physiologically relevant value. Among several experimentally observed features, the model predicts a highly nonlinear, biphasic transient behavior of eNOS activation and NO production: a rapid initial activation due to the very rapid influx of calcium into the cytosol (occurring within 1-5 min) is followed by a sustained period of activation due to protein kinases.

Nitric oxide release by deoxymyoglobin nitrite reduction during cardiac ischemia: A mathematical model

Interactions between cardiac myoglobin (Mb), nitrite, and nitric oxide (NO) are vital in regulating O₂ storage, transport, and NO homeostasis. Production of NO through the reduction of endogenous myocardial nitrite by deoxygenated myoglobin has been shown to significantly reduce myocardial infarction damage and ischemic injury. We developed a mathematical model for a cardiac arteriole and surrounding myocardium to examine the hypothesis that myoglobin switches functions from being a strong NO scavenger to an NO producer via the deoxymyoglobin nitrite reductase pathway. Our results predict that under ischemic conditions of flow, blood oxygen level, and tissue pH, deoxyMb nitrite reduction significantly elevates tissue and smooth muscle cell NO. The size of the effect is consistent at different flow rates, increases with decreasing blood oxygen and tissue pH and, in extreme pathophysiological conditions, NO can even be elevated above the normoxic levels. Our simulations suggest that cardiac deoxyMb nitrite reduction is a plausible mechanism for preserving or enhancing NO levels using endogenous nitrite despite the rate-limiting O₂ levels for endothelial NO production. This NO could then be responsible for mitigating deleterious effects under ischemic conditions.

Influence of erythrocyte aggregation at pathological levels on cell-free marginal layer in a narrow circular tube

Human red blood cells (RBCs) were perfused in a circular micro-tube (inner diameter of 25 μm) to examine the dynamic changes of cell-free marginal region at both physiological (normal) and pathophysiological (hyper) levels of RBC aggregation. The cell-free area (CFA) was measured to provide additional information on the cell-free layer (CFL) width changes in space and time domains. A prominent enhancement in the mean CFL width was found in hyper-aggregating conditions as compared to that in non-aggregating conditions (P <  0.001). The frequent contacts between RBC and the tube wall were observed and the contact frequency was greatly decreased when the aggregation level was increased from none to normal (P <  0.05) and to hyper (P <  0.001) levels. In addition, the enhanced aggregation from none to hyper levels significantly enlarged the CFA (P <  0.01). We concluded that the RBC aggregation at pathophysiological levels could promote not only the CFL width (one-dimensional parameter) but also the spatiotemporal variation of CFA (two-dimensional parameter).

Symmetry recovery of cell-free layer after bifurcations of small arterioles in reduced flow conditions: effect of RBC aggregation

Heterogeneous distribution of red blood cells (RBCs) in downstream vessels of arteriolar bifurcations can be promoted by an asymmetric formation of cell-free layer (CFL) in upstream vessels. Consequently, the CFL widths in subsequent downstream vessels become an important determinant for tissue oxygenation (O2) and vascular tone change by varying nitric oxide (NO) availability. To extend our previous understanding on the formation of CFL in arteriolar bifurcations, this study investigated the formation of CFL widths from 2 to 6 vessel-diameter (2D-6D) downstream of arteriolar bifurcations in the rat cremaster muscle (D = 51.5 ± 1.3 μm). As the CFL widths are highly influenced by RBC aggregation, the degree of aggregation was adjusted to simulate levels seen during physiological and pathological states. Our in vivo experimental results showed that the asymmetry of CFL widths persists along downstream vessels up to 6D from the bifurcating point. Moreover, elevated levels of RBC aggregation appeared to retard the recovery of CFL width symmetry. The required length of complete symmetry recovery was estimated to be greater than 11D under reduced flow conditions, which is relatively longer than interbifurcation distances of arterioles for vessel diameter of ∼50 μm. In addition, our numerical prediction showed that the persistent asymmetry of CFL widths could potentially result in a heterogeneous vasoactivity over the entire arteriolar network in such abnormal flow conditions.

Nitric oxide and the cardiovascular system

Nitric oxide (NO) generated by endothelial cells to relax vascular smooth muscle is one of the most intensely studied molecules in the past 25 years. Much of what is known about NO regulation of NO is based on blockade of its generation and analysis of changes in vascular regulation. This approach has been useful to demonstrate the importance of NO in large scale forms of regulation but provides less information on the nuances of NO regulation. However, there is a growing body of studies on multiple types of in vivo measurement of NO in normal and pathological conditions. This discussion will focus on in vivo studies and how they are reshaping the understanding of NO's role in vascular resistance regulation and the pathologies of hypertension and diabetes mellitus. The role of microelectrode measurements in the measurement of [NO] will be considered because much of the controversy about what NO does and at what concentration depends upon the measurement methodology. For those studies where the technology has been tested and found to be well founded, the concept evolving is that the stresses imposed on the vasculature in the form of flow-mediated stimulation, chemicals within the tissue, and oxygen tension can cause rapid and large changes in the NO concentration to affect vascular regulation. All these functions are compromised in both animal and human forms of hypertension and diabetes mellitus due to altered regulation of endothelial cells and formation of oxidants that both damage endothelial cells and change the regulation of endothelial nitric oxide synthase.

Erythrocyte aggregation may promote uneven spatial distribution of NO/O2 in the downstream vessel of arteriolar bifurcations

This study examined the effect of red blood cell (RBC) aggregation on nitric oxide (NO) and oxygen (O2) distributions in the downstream vessels of arteriolar bifurcations. Particular attention was paid to the inherent formation of asymmetric cell-free layer (CFL) widths in the downstream vessels and its consequential impact on the NO/O2 bioavailability after the bifurcations. A microscopic image-based two-dimensional transient model was used to predict the NO/O2 distribution by utilizing the in vivo CFL width data obtained under non-, normal- and hyper-aggregating conditions at the pseudoshear rate of 15.6±2.0s(-1). In vivo experimental result showed that the asymmetry of CFL widths was enhanced by the elevation in RBC aggregation level. The model demonstrated that NO bioavailability was regulated by the dynamic fluctuation of the local CFL widths, which is corollary to its modulation of wall shear stress. Accordingly, the uneven distribution of NO/O2 was prominent at opposite sides of the arterioles up to six vessel-diameter (6D) away from the bifurcating point, and this was further enhanced by increasing the levels of RBC aggregation. Our findings suggested that RBC aggregation potentially augments both the formation of asymmetric CFL widths and its influence on the uneven distribution of NO/O2 in the downstream flow of an arteriolar bifurcation. The extended heterogeneity of NO/O2 downstream (2D-6D) also implied its potential propagation throughout the entire arteriolar microvasculature.

Impact of stochastic fluctuations in the cell free layer on nitric oxide bioavailability

A plasma stratum (cell free layer or CFL) generated by flowing blood interposed between the red blood cell (RBC) core and the endothelium affects generation, consumption, and transport of nitric oxide (NO) in the microcirculation. CFL width is a principal factor modulating NO diffusion and vessel wall shears stress development, thus significantly affecting NO bioavailability. Since the CFL is bounded by the surface formed by the chaotically moving RBCs and the stationary but spatially non-uniform endothelial surface, its width fluctuates randomly in time and space. We analyze how these stochastic fluctuations affect NO transport in the CFL and NO bioavailability. We show that effects due to random boundaries do not average to zero and lead to an increase of NO bioavailability. Since endothelial production of NO is significantly enhanced by temporal variability of wall shear stress, we posit that stochastic shear stress stimulation of the endothelium yields the baseline continual production of NO by the endothelium. The proposed stochastic formulation captures the natural continuous and microscopic variability, whose amplitude is measurable and is of the scale of cellular dimensions. It provides a realistic model of NO generation and regulation.

Nitric oxide transport in normal human thoracic aorta: effects of hemodynamics and nitric oxide scavengers

Despite the crucial role of nitric oxide (NO) in the homeostasis of the vasculature, little quantitative information exists concerning NO transport and distribution in medium and large-sized arteries where atherosclerosis and aneurysm occur and hemodynamics is complex. We hypothesized that local hemodynamics in arteries may govern NO transport and affect the distribution of NO in the arteries, hence playing an important role in the localization of vascular diseases. To substantiate this hypothesis, we presented a lumen/wall model of the human aorta based on its MRI images to simulate the production, transport and consumption of NO in the arterial lumen and within the aortic wall. The results demonstrated that the distribution of NO in the aorta was quite uneven with remarkably reduced NO bioavailability in regions of disturbed flow, and local hemodynamics could affect NO distribution mainly via flow dependent NO production rate of endothelium. In addition, erythrocytes in the blood could moderately modulate NO concentration in the aorta, especially at the endothelial surface. However, the reaction of NO within the wall could only slightly affect NO concentration on the luminal surface, but strongly reduce NO concentration within the aortic wall. A strong positive correlation was revealed between wall shear stress and NO concentration, which was affected by local hemodynamics and NO reaction rate. In conclusion, the distribution of NO in the aorta may be determined by local hemodynamics and modulated differently by NO scavengers in the lumen and within the wall.

Vascular geometry and oxygen diffusion in the vicinity of artery-vein pairs in the kidney

Renal arterial-to-venous (AV) oxygen shunting limits oxygen delivery to renal tissue. To better understand how oxygen in arterial blood can bypass renal tissue, we quantified the radial geometry of AV pairs and how it differs according to arterial diameter and anatomic location. We then estimated diffusion of oxygen in the vicinity of arteries of typical geometry using a computational model. The kidneys of six rats were perfusion fixed, and the vasculature was filled with silicone rubber (Microfil). A single section was chosen from each kidney, and all arteries ( n = 1,628) were identified. Intrarenal arteries were largely divisible into two “types,” characterized by the presence or absence of a close physical relationship with a paired vein. Arteries with a close physical relationship with a paired vein were more likely to have a larger rather than smaller diameter, and more likely to be in the inner-cortex than the mid- or outer cortex. Computational simulations indicated that direct diffusion of oxygen from an artery to a paired vein can only occur when the two vessels have a close physical relationship. However, even in the absence of this close relationship oxygen can diffuse from an artery to periarteriolar capillaries and venules. Thus AV oxygen shunting in the proximal preglomerular circulation is dominated by direct diffusion of oxygen to a paired vein. In the distal preglomerular circulation, it may be sustained by diffusion of oxygen from arteries to capillaries and venules close to the artery wall, which is subsequently transported to renal veins by convection.

Two-dimensional transient model for prediction of arteriolar NO/O2 modulation by spatiotemporal variations in cell-free layer width

Despite the significant roles of the cell-free layer (CFL) in balancing nitric oxide (NO) and oxygen (O2) bioavailability in arteriolar tissue, many previous numerical approaches have relied on a one-dimensional (1-D) steady-state model for simplicity. However, these models are unable to demonstrate the influence of spatiotemporal variations in the CFL on the NO/O2 transport under dynamic flow conditions. Therefore, the present study proposes a new two-dimensional (2-D) transient model capable of predicting NO/O2 transport modulated by the spatiotemporal variations in the CFL width. Our model predicted that NO bioavailability was inversely related to the CFL width as expected. The enhancement of NO production by greater wall shear stress with a thinner CFL could dominate the diffusion barrier role of the CFL. In addition, NO/O2 availability along the vascular wall was inhomogeneous and highly regulated by dynamic changes of local CFL width variation. The spatial variations of CFL widths on opposite sides of the arteriole exhibited a significant inverse relation. This asymmetric formation of CFL resulted in a significantly imbalanced NO/O2 bioavailability on opposite sides of the arteriole. The novel integrative methodology presented here substantially highlighted the significance of spatiotemporal variations of the CFL in regulating the bioavailability of NO/O2, and provided further insight about the opposing effects of the CFL on arteriolar NO production.

Nitric oxide transport in blood: a third gas in the respiratory cycle

The trapping, processing, and delivery of nitric oxide (NO) bioactivity by red blood cells (RBCs) have emerged as a conserved mechanism through which regional blood flow is linked to biochemical cues of perfusion sufficiency. We present here an expanded paradigm for the human respiratory cycle based on the coordinated transport of three gases: NO, O₂, and CO₂. By linking O₂ and NO flux, RBCs couple vessel caliber (and thus blood flow) to O₂ availability in the lung and to O₂ need in the periphery. The elements required for regulated O₂-based signal transduction via controlled NO processing within RBCs are presented herein, including S-nitrosothiol (SNO) synthesis by hemoglobin and O₂-regulated delivery of NO bioactivity (capture, activation, and delivery of NO groups at sites remote from NO synthesis by NO synthase). The role of NO transport in the respiratory cycle at molecular, microcirculatory, and system levels is reviewed. We elucidate the mechanism through which regulated NO transport in blood supports O₂ homeostasis, not only through adaptive regulation of regional systemic blood flow but also by optimizing ventilation-perfusion matching in the lung. Furthermore, we discuss the role of NO transport in the central control of breathing and in baroreceptor control of blood pressure, which subserve O₂ supply to tissue. Additionally, malfunctions of this transport and signaling system that are implicated in a wide array of human pathophysiologies are described. Understanding the (dys)function of NO processing in blood is a prerequisite for the development of novel therapies that target the vasoactive capacities of RBCs.

A review of numerical methods for red blood cell flow simulation

In this review, we provide an overview of the simulation techniques employed for modelling the flow of red blood cells (RBCs) in blood plasma. The scope of this review omits the fluid modelling aspect while focusing on other key components in the RBC-plasma model such as (1) describing the RBC deformation with shell-based and spring-based RBC models, (2) constitutive models for RBC aggregation based on bridging theory and depletion theory and (3) additional strategies required for completing the RBC-plasma flow model. These include topics such as modelling fluid-structure interaction with the immersed boundary method and boundary integral method, and updating the variations in multiphase fluid property through the employment of index field methods. Lastly, we summarily discuss the current state and aims of RBC modelling and suggest some research directions for the further development of this field of modelling.

Two-phase model for prediction of cell-free layer width in blood flow

This study aimed to develop a numerical model capable of predicting changes in the cell-free layer (CFL) width in narrow tubes with consideration of red blood cell aggregation effects. The model development integrates to empirical relations for relative viscosity (ratio of apparent viscosity to medium viscosity) and core viscosity measured on independent blood samples to create a continuum model that includes these two regions. The constitutive relations were derived from in vitro experiments performed with three different glass-capillary tubes (inner diameter=30, 50 and 100 μm) over a wide range of pseudoshear rates (5-300 s(-1)). The aggregation tendency of the blood samples was also varied by adding Dextran 500 kDa. Our model predicted that the CFL width was strongly modulated by the relative viscosity function. Aggregation increased the width of CFL, and this effect became more pronounced at low shear rates. The CFL widths predicted in the present study at high shear conditions were in agreement with those reported in previous studies. However, unlike previous multi-particle models, our model did not require a high computing cost, and it was capable of reproducing results for a thicker CFL width at low shear conditions, depending on aggregating tendency of the blood.

Local oxidative and nitrosative stress increases in the microcirculation during leukocytes-endothelial cell interactions

Leukocyte-endothelial cell interactions and leukocyte activation are important factors for vascular diseases including nephropathy, retinopathy and angiopathy. In addition, endothelial cell dysfunction is reported in vascular disease condition. Endothelial dysfunction is characterized by increased superoxide (O₂^•−) production from endothelium and reduction in NO bioavailability. Experimental studies have suggested a possible role for leukocyte-endothelial cell interaction in the vessel NO and peroxynitrite levels and their role in vascular disorders in the arterial side of microcirculation. However, anti-adhesion therapies for preventing leukocyte-endothelial cell interaction related vascular disorders showed limited success. The endothelial dysfunction related changes in vessel NO and peroxynitrite levels, leukocyte-endothelial cell interaction and leukocyte activation are not completely understood in vascular disorders. The objective of this study was to investigate the role of endothelial dysfunction extent, leukocyte-endothelial interaction, leukocyte activation and superoxide dismutase therapy on the transport and interactions of NO, O₂^•− and peroxynitrite in the microcirculation. We developed a biotransport model of NO, O₂^•− and peroxynitrite in the arteriolar microcirculation and incorporated leukocytes-endothelial cell interactions. The concentration profiles of NO, O₂^•− and peroxynitrite within blood vessel and leukocytes are presented at multiple levels of endothelial oxidative stress with leukocyte activation and increased superoxide dismutase accounted for in certain cases. The results showed that the maximum concentrations of NO decreased ∼0.6 fold, O₂^•− increased ∼27 fold and peroxynitrite increased ∼30 fold in the endothelial and smooth muscle region in severe oxidative stress condition as compared to that of normal physiologic conditions. The results show that the onset of endothelial oxidative stress can cause an increase in O₂^•− and peroxynitrite concentration in the lumen. The increased O₂^•− and peroxynitrite can cause leukocytes priming through peroxynitrite and leukocytes activation through secondary stimuli of O₂^•− in bloodstream without endothelial interaction. This finding supports that leukocyte rolling/adhesion and activation are independent events.

Nitric oxide transport in an axisymmetric stenosis

To test the hypothesis that disturbed flow can impede the transport of nitric oxide (NO) in the artery and hence induce atherogenesis, we used a lumen-wall model of an idealized arterial stenosis with NO produced at the blood vessel-wall interface to study the transport of NO in the stenosis. Blood flows in the lumen and through the arterial wall were simulated by Navier-Stokes equations and Darcy's Law, respectively. Meanwhile, the transport of NO in the lumen and the transport of NO within the arterial wall were modelled by advection-diffusion reaction equations. Coupling of fluid dynamics at the endothelium was achieved by the Kedem-Katchalsky equations. The results showed that both the hydraulic conductivity of the endothelium and the non-Newtonian viscous behaviour of blood had little effect on the distribution of NO. However, the blood flow rate, stenosis severity, red blood cells (RBCs), RBC-free layer and NO production rate at the blood vessel-wall interface could significantly affect the transport of NO. The theoretical study revealed that the transport of NO was significantly hindered in the disturbed flow region distal to the stenosis. The reduced NO concentration in the disturbed flow region might play an important role in the localized genesis and development of atherosclerosis.

PEG-albumin supraplasma expansion is due to increased vessel wall shear stress induced by blood viscosity shear thinning

We studied the extreme hemodilution to a hematocrit of 11% induced by three plasma expanders: polyethylene glycol (PEG)-conjugated albumin (PEG-Alb), 6% 70-kDa dextran, and 6% 500-kDa dextran. The experimental component of our study relied on microelectrodes and cardiac output to measure both the rheological properties of plasma-expander blood mixtures and nitric oxide (NO) bioavailability in vessel walls. The modeling component consisted of an analysis of the distribution of wall shear stress (WSS) in the microvessels. Our experiments demonstrated that plasma expansion with PEG-Alb caused a state of supraperfusion with cardiac output 40% above baseline, significantly increased NO vessel wall bioavailability, and lowered peripheral vascular resistance. We attributed this behavior to the shear thinning nature of blood and PEG-Alb mixtures. To substantiate this hypothesis, we developed a mathematical model of non-Newtonian blood flow in a vessel. Our model used the Quemada rheological constitutive relationship to express blood viscosity in terms of both hematocrit and shear rate. The model revealed that the net effect of the hemodilution induced by relatively low-viscosity shear thinning PEG-Alb plasma expanders is to reduce overall blood viscosity and to increase the WSS, thus intensifying endothelial NO production. These changes act synergistically, significantly increasing cardiac output and perfusion due to lowered overall peripheral vascular resistance.

Nitric oxide signaling in the microcirculation

Several apparent paradoxes are evident when one compares mathematical predictions from models of nitric oxide (NO) diffusion and convection in vasculature structures with experimental measurements of NO (or related metabolites) in animal and human studies. Values for NO predicted from mathematical models are generally much lower than in vivo NO values reported in the literature for experiments, specifically with NO microelectrodes positioned at perivascular locations next to different sizes of blood vessels in the microcirculation and NO electrodes inserted into a wide range of tissues supplied by the microcirculation of each specific organ system under investigation. There continues to be uncertainty about the roles of NO scavenging by hemoglobin versus a storage function that may conserve NO, and other signaling targets for NO need to be considered. This review describes model predictions and relevant experimental data with respect to several signaling pathways in the microcirculation that involve NO.

Impact of endothelium roughness on blood flow

Cell free layer (CFL), a plasma layer bounded by the red blood cell (RBC) core and the endothelium, plays an important physiological role. Its width affects the effective blood viscosity as well as the scavenging and production of nitric oxide (NO). Measurements of the CFL and its spatio-temporal variability are highly uncertain, exhibiting random fluctuations. Yet traditional models of blood flow and NO scavenging treat the CFL's bounding surfaces as deterministic and smooth. We investigate the effects of the endothelium roughness and uncertain (random) spatial variability on blood flow and the estimates of effective blood viscosity.

Simulation of NO and O2 transport facilitated by polymerized hemoglobin solutions in an arteriole that takes into account wall shear stress-induced NO production

A mathematical model was developed to study nitric oxide (NO) and oxygen (O(2)) transport in an arteriole and surrounding tissues exposed to a mixture of red blood cells (RBCs) and hemoglobin (Hb)-based O(2) carriers (HBOCs). A unique feature of this model is the inclusion of blood vessel wall shear stress-induced production of endothelial-derived NO, which is very sensitive to the viscosity of the RBC and HBOC mixture traversing the blood vessel lumen. Therefore in this study, a series of polymerized bovine Hb (PolyHb) solutions with high viscosity, varying O(2) affinities, NO dioxygenation rate constants and O(2) dissociation rate constants that were previously synthesized and characterized by our group was evaluated via mathematical modeling, in order to investigate the effect of these biophysical properties on the transport of NO and O(2) in an arteriole and its surrounding tissues subjected to anemia with the commercial HBOC Oxyglobin® and cell-free bovine Hb (bHb) serving as appropriate controls. The computer simulation results indicated that transfusion of high viscosity PolyHb solutions promoted blood vessel wall shear stress dependent generation of the vasodilator NO, especially in the blood vessel wall and should transport enough NO inside the smooth muscle layer to activate vasodilation compared to the commercial HBOC Oxyglobin® and cell-free bHb. However, NO scavenging in the arteriole lumen was unavoidable due to the intrinsic high NO dioxygenation rate constant of the HBOCs being studied. This study also observed that all PolyHbs could potentially improve tissue oxygenation under hypoxic conditions, while low O(2) affinity PolyHbs were more effective in oxygenating tissues under normoxic conditions compared with high O(2) affinity PolyHbs. In addition, all ultrahigh molecular weight PolyHbs displayed higher O(2) transfer rates than the commercial HBOC Oxyglobin® and cell-free bHb. Therefore, these results suggest that ultrahigh molecular weight PolyHb solutions could be used as safe and efficacious O(2) carriers for use in transfusion medicine. It also suggests that future generations of PolyHb solutions should possess lower NO dioxygenation reaction rate constants in order to reduce NO scavenging, while maintaining high solution viscosity to take advantage of wall shear stress-induced NO production. Taken together, we suggest that this mathematical model can be used to predict the vasoactivity of HBOCs and help guide the design and optimization of the next generation of HBOCs for use in transfusion medicine.

Effects of cell-free layer formation on NO/O2 bioavailability in small arterioles

We developed a new time-dependent computational model for coupled NO/O(2) transport in small arterioles that incorporates potential physiological responses (temporal changes in NO scavenging rate and O(2) partial pressure in blood lumen and NO production rate in endothelium) to the temporal cell-free layer width variations. Two relations between wall shear stress (WSS) and NO production rate based on the linear and sigmoidal functions were considered in this simulation study. The cell-free layer data used for the simulation were acquired from arteriolar flows (D=48.3 ± 1.9 μm) in the rat cremaster muscles under normal flow conditions (WSS=3.4-5.6 Pa). For both cases of linear and sigmoidal relations, temporal layer width variations were found to be capable of significantly enhancing NO bioavailability and this effect was more pronounced in the latter (P<0.0005) than the former (P<0.005). In contrast, O(2) bioavailability in the arteriolar wall was not considerably altered by the temporal layer width variations, irrespective of the relation. Prominent enhancement (P<0.005) of soluble guanylyl cyclase (sGC) activation in the smooth muscle by the temporal layer width variations were predicted for both relations. The extent of sGC activation was generally lower (P<0.01) in the case of the sigmoidal relation than that of the linear relation, suggesting a lesser tendency for arterioles to dilate with the former.

Modeling O₂-dependent effects of nitrite reductase activity in blood and tissue on coupled NO and O₂ transport around arterioles

Recent evidence in the literature suggests that tissues play a greater role than blood in reducing nitrite to NO under ischemic or hypoxic conditions. Our previous mathematical model for coupled NO and O(2) transport around an arteriole, modified to include superoxide generation from dysfunctional endothelium, was developed further to include nitrite reductase activity in blood and tissue. Steady-state radial and axial NO and pO(2) profiles in the arteriole and surrounding tissue were simulated for different blood flow rates and arterial blood pO(2) values. The resulting computer simulations demonstrate that nitrite reductase activity in blood is not a very effective mechanism for conserving NO due to the strong scavenging of NO by hemoglobin. In contrast, nitrite reductase activity in tissue is much more effective in increasing NO bioavailability in the vascular wall and contributes progressively more NO as tissue hypoxia becomes more severe.

A mathematical model of diffusional shunting of oxygen from arteries to veins in the kidney

To understand how arterial-to-venous (AV) oxygen shunting influences kidney oxygenation, a mathematical model of oxygen transport in the renal cortex was created. The model consists of a multiscale hierarchy of 11 countercurrent systems representing the various branch levels of the cortical vasculature. At each level, equations describing the reactive-advection-diffusion of oxygen are solved. Factors critical in renal oxygen transport incorporated into the model include the parallel geometry of arteries and veins and their respective sizes, variation in blood velocity in each vessel, oxygen transport (along the vessels, between the vessels and between vessel and parenchyma), nonlinear binding of oxygen to hemoglobin, and the consumption of oxygen by renal tissue. The model is calibrated using published measurements of cortical vascular geometry and microvascular Po2. The model predicts that AV oxygen shunting is quantitatively significant and estimates how much kidney V̇o2 must change, in the face of altered renal blood flow, to maintain cortical tissue Po2 at a stable level. It is demonstrated that oxygen shunting increases as renal V̇o2 or arterial Po2 increases. Oxygen shunting also increases as renal blood flow is reduced within the physiological range or during mild hemodilution. In severe ischemia or anemia, or when kidney V̇o2 increases, AV oxygen shunting in proximal vascular elements may reduce the oxygen content of blood destined for the medullary circulation, thereby exacerbating the development of tissue hypoxia. That is, cortical ischemia could cause medullary hypoxia even when medullary perfusion is maintained. Cortical AV oxygen shunting limits the change in oxygen delivery to cortical tissue and stabilizes tissue Po2 when arterial Po2 changes, but renders the cortex and perhaps also the medulla susceptible to hypoxia when oxygen delivery falls or consumption increases.

Integration of cardiovascular regulation by the blood/endothelium cell-free layer

The cell-free layer (CFL) width separating red blood cells in flowing blood from the endothelial cell membrane is shown to be a regulator of the balance between nitric oxide (NO) production by the endothelium and NO scavenging by blood hemoglobin. The CFL width is determined by hematocrit (Hct) and the vessel wall flow velocity gradient. These factors and blood and plasma viscosity determine vessel wall shear stress which regulates the production of NO in the vascular wall. Mathematical modeling and experimental findings show that vessel wall NO concentration is a strong nonlinear function of Hct and that small Hct variations have comparatively large effects on blood pressure regulation. Furthermore, NO concentration is a regulator of inflammation and oxygen metabolism. Therefore, small, sustained perturbations of Hct may have long-term effects that can promote pro-hypertensive and pro-inflammatory conditions. In this context, Hct and its variability are directly related to vascular tone, peripheral vascular resistance, oxygen transport and delivery, and inflammation. These effects are relevant to the analysis and understanding of blood pressure regulation, as NO bioavailability regulates the contractile state of blood vessels. Furthermore, regulation of the CFL is a direct function of blood composition therefore understanding of its physiology relates to the design and management of fluid resuscitation fluids. From a medical perspective, these studies propose that it should be of clinical interest to note small variations in patient's Hct levels given their importance in modulating the CFL width and therefore NO bioavailability. WIREs Syst Biol Med 2011 3 458-470 DOI: 10.1002/wsbm.150

Influence of tissue metabolism and capillary oxygen supply on arteriolar oxygen transport: a computational model

We present a theoretical model for steady-state radial and longitudinal oxygen transport in arterioles containing flowing blood (plasma and red blood cells) and surrounded by living tissue. This model combines a detailed description of convective and diffusive oxygen transport inside the arteriole with a novel boundary condition at the arteriolar lumen surface, and the results provide new mass transfer coefficients for computing arteriolar O(2) losses based on far-field tissue O(2) tension and in the presence of spatially distributed capillaries. A numerical procedure is introduced for calculating O(2) diffusion from an arteriole to a continuous capillary-tissue matrix immediately adjacent to the arteriole. The tissue O(2) consumption rate is assumed to be constant and capillaries act as either O(2) sources or sinks depending on the local O(2) environment. Using the model, O(2) saturation (SO(2)) and tension (PO(2)) are determined for the intraluminal region of the arteriole, as well as for the extraluminal region in the neighbouring tissue. Our model gives results that are consistent with available experimental data and previous intraluminal transport models, including appreciable radial decreases in intraluminal PO(2) for all vessel diameters considered (12-100 μm) and slower longitudinal decreases in PO(2) for larger vessels than for smaller ones, and predicts substantially less diffusion of O(2) from arteriolar blood than do models with PO(2) specified at the edge of the lumen. The dependence of the new mass transfer coefficients on vessel diameter, SO(2) and far-field PO(2) is calculated allowing their application to a wide range of physiological situations. This novel arteriolar O(2) transport model will be a vital component of future integrated models of microvascular regulation of O(2) supply to capillary beds and the tissue regions they support.

3D network model of NO transport in tissue

We developed a mathematical model to simulate shear stress-dependent nitric oxide (NO) production and transport in a 3D microcirculatory network based on published data. The model consists of a 100 μm × 500 μm × 75 μm rectangular volume of tissue containing two arteriole-branching trees, and nine capillaries surrounding the vessels. Computed distributions for NO in blood, vascular walls, and surrounding tissue were affected by hematocrit (Hct) and wall shear stress (WSS) in the network. The model demonstrates that variations in the red blood cell (RBC) distribution and WSS in a branching network can have differential effects on computed NO concentrations due to NO consumption by RBCs and WSS-dependent changes in NO production. The model predicts heterogeneous distributions of WSS in the network. Vessel branches with unequal blood flow rates gave rise to a range of WSS values and therefore NO production rates. Despite increased NO production in a branch with higher blood flow and WSS, vascular wall NO was predicted to be lower due to greater NO consumption in blood, since the microvascular Hct increased with redistribution of RBCs at the vessel bifurcation. Within other regions, low WSS was combined with decreased NO consumption to enhance the NO concentration.

Temporal variations of the cell-free layer width may enhance NO bioavailability in small arterioles: Effects of erythrocyte aggregation

Recently, we have shown that temporal variations in the cell-free layer width can potentially enhance nitric oxide (NO) bioavailability in small arterioles. Since the layer width variations can be augmented by red blood cell aggregation, we tested the hypothesis that an increase in the layer width variations due to red blood cell aggregation could provide an underlying mechanism to improve NO bioavailability in the endothelium and promote vasodilatory effects. Utilizing cell-free layer width data acquired from arterioles of the rat cremaster muscle before and after dextran infusion in reduced flow conditions (wall shear stress=0.13-0.24Pa), our computational model predicted exponential enhancements of NO bioavailability in the endothelium and soluble guanylyl cyclase (sGC) activation in the smooth muscle layer with increasing temporal variability of the layer width. These effects were mediated primarily by the transient responses of wall shear stress and NO production rate to the layer width variations. The temporal variations in the layer width were significantly enhanced (P<0.05) by aggregation, leading to significant improvements (P<0.05) in NO bioavailability and sGC activation. As a result, the significant reduction (P<0.05) of sGC activation due to the increased width of the layer after aggregation induction was diminished by the opposing effect of the layer variations. These findings highlighted the possible enhancement of NO bioavailability and vascular tone in the arteriole by the augmented layer width variations due to the aggregation.

The effect of small changes in hematocrit on nitric oxide transport in arterioles

We report the development of a mathematical model that quantifies the effects of small changes in systemic hematocrit (Hct) on the transport of nitric oxide (NO) in the microcirculation. The model consists of coupled transport equations for NO and oxygen (O2) and accounts for both shear-induced NO production by the endothelium and the effect of changing systemic Hct on the rate of NO production and the rate of NO scavenging by red blood cells. To incorporate the dependence of the plasma layer width on changes in Hct, the model couples the hemodynamics of blood in arterioles with NO and O2 transport in the plasma layer. A sensitivity analysis was conducted to determine the effects of uncertain model parameters (the thicknesses of endothelial surface layers and diffusion coefficients of NO and O2 in muscle tissues and vascular walls) on the model's predictions. Our analysis reveals that small increases in Hct may raise NO availability in the vascular wall. This finding sheds new light on the experimental data that show that the blood circulation responds to systematic increases of Hct in a manner that is consistent with increasing NO production followed by a plateau.

Modulation of NO bioavailability by temporal variation of the cell-free layer width in small arterioles

The cell-free layer exhibits dynamic characteristics in the time domain that may be capable of altering nitric oxide (NO) bioavailability in small arterioles. However, this effect has not been fully elucidated. This study utilized a computational model on NO transport to predict how temporal variations in the layer width could modulate NO bioavailability in the arterioles. Data on the layer width was acquired from high-speed video recordings in arterioles (ID = 48.4 ± 1.8 μm) of the rat cremaster muscle. We found that when wall shear stress response was not considered, the layer variability could lead to a slight decrease (1.6-6.6%) in NO bioavailability that was independent of transient changes in NO scavenging rate. Conversely, the transient response in wall shear stress and NO production rate played a dominant role in reversing this decline such that a significant augmentation (5.3-21.0%) in NO bioavailability was found with increasing layer variability from 24.6 to 63.8%. This study highlighted the importance of the temporal changes in wall shear stress and NO production rate caused by the layer width variations in prediction of NO bioavailability in arterioles.

A computational model for nitric oxide, nitrite and nitrate biotransport in the microcirculation: effect of reduced nitric oxide consumption by red blood cells and blood velocity

Bioavailability of vasoactive endothelium-derived nitric oxide (NO) in vasculature is a critical factor in regulation of many physiological processes. Consumption of NO by RBC plays a crucial role in maintaining NO bioavailability. Recently, Deonikar and Kavdia (2009b) reported an effective NO-RBC reaction rate constant of 0.2×10(5)M(-1)s(-1) that is ~7 times lower than the commonly used NO-RBC reaction rate constant of 1.4×10(5)M(-1)s(-1). To study the effect of lower NO-RBC reaction rate constant and nitrite and nitrate formation (products of NO metabolism in blood), we developed a 2D mathematical model of NO biotransport in 50 and 200μm ID arterioles to calculate NO concentration in radial and axial directions in the vascular lumen and vascular wall of the arterioles. We also simulated the effect of blood velocity on NO distribution in the arterioles to determine whether NO can be transported to downstream locations in the arteriolar lumen. The results indicate that lowering the NO-RBC reaction rate constant increased the NO concentration in the vascular lumen as well as the vascular wall. Increasing the velocity also led to increase in NO concentration. We predict increased NO concentration gradient along the axial direction with an increase in the velocity. The predicted NO concentration was 281-1163nM in the smooth muscle cell layer for 50μm arteriole over the blood velocity range of 0.5-4cms(-1) for k(NO-RBC) of 0.2×10(5)M(-1)s(-1), which is much higher than the reported values from earlier mathematical modeling studies. The NO concentrations are similar to the experimentally measured vascular wall NO concentration range of 300-1000nM in several different vascular beds. The results are significant from the perspective that the downstream transport of NO is possible under the right circumstances.

Effect of cell-free layer variation on arteriolar wall shear stress

Relationship between a cell-free layer and wall shear stress (WSS) in small arterioles has been of interest in microcirculatory research. However, influence of temporal variation in the cell-free layer width on the WSS in vivo has not been fully elucidated. In this study, we tested the hypothesis that the layer variation would increase the WSS, and this effect would be enhanced by red blood cell aggregation. The cell-free layer width in arterioles (29.5–67.1 μm ID) in rat cremaster muscles were obtained with a high-speed video camera, and the layer width data were introduced into WSS estimation. Dextran 500 was administrated to elevate the aggregation level of red blood cells to those seen in normal human blood. The variation of the layer was quantified by the variability (coefficient of variation), and its effect on WSS was studied under normal and reduced flow conditions. We found that the dextran-induced red blood cell aggregation significantly elevated the variability (p < 0.01) at low pseudoshear rates of 9.2 ± 0.6 s⁻¹. The WSS estimated without taking account of the variability showed underestimation of its value than that of with consideration of the variability under all flow conditions, and this effect became more pronounced with increasing the variability. The variation of the cell-free layer should, therefore, be considered in the determination of the WSS particularly in the presence of red blood cell aggregation under reduced flow condition.

The variability of blood pressure due to small changes of hematocrit

The hematocrit (Hct) of awake hamsters was lowered to 90% of baseline by isovolemic hemodilution using hamster plasma to determine the acute effect of small changes in Hct and blood viscosity on systemic hemodynamics. Mean arterial blood pressure increased, reaching a maximum of about 10% above baseline (8.6 +/- 5.5 mmHg) when Hct decreased 8.4 +/- 1.9% (P < 0.005). Cardiac output increased continuously with hemodilution. These conditions were reached at approximately 60 min after exchange transfusion and remained stationary for 1 h. Peripheral vascular resistance was approximately constant up to a decrease of Hct of about 10% and then fell continuously with lowering Hct. Vascular hindrance or vascular resistance independent of blood viscosity increased by about 20% and remained at this level up to an Hct decrease of 20%, indicating that the vasculature constricted with the lowered Hct. The results for the initial 2-h period are opposite but continuous with previous findings with small increases in Hct. In conclusion, limited acute anemic conditions increase mean arterial blood pressure during the initial period of 2 h, an effect that is quantitatively similar but opposite to the acute increase of Hct during the same period.

Cerebral oxygen delivery and consumption during evoked neural activity

Increases in neural activity evoke increases in the delivery and consumption of oxygen. Beyond observations of cerebral tissue and blood oxygen, the role and properties of cerebral oxygen delivery and consumption during changes in brain function are not well understood. This work overviews the current knowledge of functional oxygen delivery and consumption and introduces recent and preliminary findings to explore the mechanisms by which oxygen is delivered to tissue as well as the temporal dynamics of oxygen metabolism. Vascular oxygen tension measurements have shown that a relatively large amount of oxygen exits pial arterioles prior to capillaries. Additionally, increases in cerebral blood flow (CBF) induced by evoked neural activation are accompanied by arterial vasodilation and also by increases in arteriolar oxygenation. This increase contributes not only to the down-stream delivery of oxygen to tissue, but also to delivery of additional oxygen to extra-vascular spaces surrounding the arterioles. On the other hand, the changes in tissue oxygen tension due to functional increases in oxygen consumption have been investigated using a method to suppress the evoked CBF response. The functional decreases in tissue oxygen tension induced by increases in oxygen consumption are slow to evoked changes in CBF under control conditions. Preliminary findings obtained using flavoprotein autofluorescence imaging suggest cellular oxidative metabolism changes at a faster rate than the average changes in tissue oxygen. These issues are important in the determination of the dynamic changes in tissue oxygen metabolism from hemoglobin-based imaging techniques such as blood oxygenation-level dependent functional magnetic resonance imaging (fMRI).

Functional optical imaging at the microscopic level

Functional microscopic imaging of in vivo tissues aims at characterizing parameters at the level of the unitary cellular components under normal conditions, in the presence of blood flow, to understand and monitor phenomena that lead to maintaining homeostatic balance. Of principal interest are the setting of shear stress on the endothelium; formation of the plasma layer, where the balance between nitric oxide production and scavenging is established; and formation of the oxygen gradients that determine the distribution of oxygen from blood into the tissue. Optical techniques that enable the analysis of functional microvascular processes are the measurement of blood vessel dimensions by image shearing, the photometric analysis of the extent of the plasma layer, the dual-slit methodology for measuring blood flow velocity, and the direct measurement of oxygen concentration in blood and tissue. Each of these technologies includes the development of paired, related mathematical approaches that enable characterizing the transport properties of the blood tissue system. While the technology has been successful in analyzing the living tissue in experimental conditions, deployment to clinical settings remains an elusive goal, due to the difficulty of obtaining optical access to the depth of the tissue.

Extracellular diffusion and permeability effects on NO-RBCs interactions using an experimental and theoretical model

Nitric oxide (NO) is a potent vasodilator and its homeostasis depends on interaction with RBCs. A key factor in understanding NO-RBC interactions in vascular lumen is a comprehensive analysis of product identification and quantification. In this context, administration of NO during in vitro NO-RBC interactions becomes a crucial variable. In this study, we designed a bioreactor that maintains a precise NO concentration in the headspace that diffuses to RBCs suspension to study the quantitative effect of NO concentration and hematocrit (Hct) on NO-RBC interactions. The products of NO-RBC reaction (nitrite and total nitrogen species (total NOx)) were measured by chemiluminescence assay. A mathematical model simulating NO biotransport to a single RBC was developed to (1) estimate NO-RBC reaction rate constant; (2) predict the NO concentrations in the bulk RBC suspension and at the RBC membrane for RBC membrane NO permeability (P(m)) values of 0.0415-40 cm/s. Measured nitrite and total NOx concentrations increased with increase in headspace NO concentration whereas nitrite concentrations decreased with hematocrit and total NOx concentrations increased with hematocrit. This indicates that the extracellular resistance is a controlling factor for RBC uptake of NO. Modeling results showed that the effective reaction rate constant (k(eff)) for NO-RBC interactions was 2.32 x 10(4)-1.08 x 10(6) M(-1) s(-1). Results also predict that the membrane permeability in the range of 0.0415-0.4 cm/s is required to maintain physiologically relevant levels of NO at the smooth muscle cell layer. The effective reaction rate constant increased with increase in P(m) and magnitude of increase was higher at 45% Hct. For all P(m) values, the k(hb)/k(eff) ratios were lower for 45% Hct as compared to 5% Hct indicating extracellular resistance is important for RBC NO uptake. Our experimental and mathematical analyses of NO-RBC interactions indicate that both unstirred layer and RBC membrane have a significant effect on NO transport to RBCs. In addition, the membrane permeability in the range of 0.0415-0.4 cm/s is required to maintain sufficient NO concentrations at the smooth muscle cell layer.

Transfer of nitric oxide by blood from upstream to downstream resistance vessels causes microvascular dilation

The discovery that hemoglobin, albumin, and glutathione carry and release nitric oxide (NO) may have consequences for movement of NO by blood within microvessels. We hypothesize that NO in plasma or bound to proteins likely survives to downstream locations. To confirm this hypothesis, there must be a finite NO concentration ([NO]) in arteriolar blood, and upstream resistance vessels must be able to increase the vessel wall [NO] of downstream arterioles. Arteriolar blood NO was measured with NO-sensitive microelectrodes, and vessel wall [NO] was consistently 25-40% higher than blood [NO]. Localized suppression of NO production in large arterioles over 500-1,000 microm with L-nitroarginine reduced the [NO] approximately 40%, indicating as much as 60% of the wall NO was from blood transfer. Flow in mesenteric arteries was elevated by occlusion of adjacent arteries to induce a flow-mediated increase in arterial NO production. Both arterial wall and downstream arteriolar [NO] increased and the arterioles dilated as the blood [NO] was increased. To study receptor-mediated NO generation, bradykinin was locally applied to upstream large arterioles and NO measured there and in downstream arterioles. At both sites, [NO] increased and both sets of vessels dilated. When isoproterenol was applied to the upstream vessels, they dilated, but neither the [NO] or diameter downstream arterioles increased. These observations indicate that NO can move in blood from upstream to downstream resistance vessels. This mechanism allows larger vessels that generate large [NO] to influence vascular tone in downstream vessels in response to both flow and receptor stimuli.

Mathematical model of NO and O2 transport in an arteriole facilitated by hemoglobin based O2 carriers

The increasing demand for donated human blood has spurred research to develop hemoglobin-based O(2) carriers (HBOCs) that can be used as red blood cell (RBC) substitutes. However, in vivo studies of acellular HBOCs have shown an increase in mean arterial pressure following transfusion that has been attributed to the HBOC's ability to scavenge NO (an important vasodilator that is synthesized by endothelial cells in the blood vessel wall that signals neighboring smooth muscle cells to relax). In this study, a mathematical model was developed to describe NO and O(2) transport in an arteriole containing a mixture of acellular HBOCs and RBCs. The acellular HBOCs studied in this work possessed a wide range of O(2) affinities, O(2) dissociation rate constants and NO reactivities in order to evaluate their effect on O(2) tension and NO concentration in the arteriole tissue region. By focusing on the concentration of NO that is localized in the arteriole smooth muscle cell region, the model can predict the vasopressor response of HBOCs. The results of this study confirmed that acellular HBOCs scavenge large amounts of NO from the entire arteriole (approximately 50% or more NO compared to RBCs only). A recombinant Hb, rHb3011, displayed the least NO reactivity and consequently left the most NO remaining in the arteriole. The NO concentration in the arteriole with respect to the other HBOCs studied was proportional to their NO reactivity. Therefore, the results of this study demonstrate that NO scavenging is an unavoidable consequence of transfusing HBOCs. To prevent or reduce vasodilatation, we suggest administration of NO by either inhaling NO or transfusing nitrite into the blood stream followed by transfusion of HBOC.

Mathematical modeling of the interaction between oxygen, nitric oxide and superoxide

Computer simulations were performed based on a multiple chemical species convection-diffusion model with coupled biochemical reactions for oxygen (O2), nitric oxide (NO), superoxide (O2*-), peroxynitrite (ONOO-), nitrite (NO2-) and nitrate (NO3-) in cylindrical geometry with blood flow through a 30 microm diameter arteriole. Steady state concentration gradients of all chemical species were predicted for different O2*- production rates, superoxide dismutase (SOD) concentrations, and blood flow rates. Effects of additional O2*- production from dysfunctional endothelial nitric oxide synthase (eNOS) were also simulated. The model predicts that convection is essential for characterizing O2 partial pressure gradients (PO2) in the bloodstream and surrounding tissue, but has little direct effect on NO gradients in blood and tissue.

A computational model of nitric oxide production and transport in a parallel plate flow chamber

We developed a mathematical model to investigate the production and transport of nitric oxide (NO) generated by a monolayer of cultured endothelial cells exposed to flow in a parallel plate flow chamber. The objectives were to provide a theoretical framework for interpreting experimental observations and to suggest a quantitative relationship between shear stress and NO production rate. NO production was described as a combination of a basal production rate term and a shear-dependent term. Our results show that the shear stress-dependence of the production of NO by the endothelium influences the nature of mass transport within the boundary layer. We found that the steady state NO concentration near the endothelial surface exhibits a biphasic dependence on shear stress, in which at low flow, NO concentration decreases owing to the enhanced removal by convective transport while only at higher shear stresses does the increased production cause an increase in NO concentration. The unsteady response to step changes in flow exhibits transient fluctuations in NO that can be explained by time-dependent changes in the diffusive and convective mass transport as the concentration profile evolves. Our results indicate that this model can be used to determine the relationship between shear stress and NO production rate from measurements of NO concentration.

Nitric oxide in the vasculature: where does it come from and where does it go? A quantitative perspective

Nitric oxide (NO) affects two key aspects of O2 supply and demand: It regulates vascular tone and blood flow by activating soluble guanylate cyclase (sGC) in the vascular smooth muscle, and it controls mitochondrial O2 consumption by inhibiting cytochrome c oxidase. However, significant gaps exist in our quantitative understanding of the regulation of NO production in the vascular region. Large apparent discrepancies exist among the published reports that have analyzed the various pathways in terms of the perivascular NO concentration, the efficacy of NO in causing vasodilation (EC50), its efficacy in tissue respiration (IC50), and the paracrine and endocrine NO release. In this study, we review the NO literature, analyzing NO levels on various scales, identifying and analyzing the discrepancies in the reported data, and proposing hypotheses that can potentially reconcile these discrepancies. Resolving these issues is highly relevant to improving our understanding of vascular biology and to developing pharmaceutical agents that target NO pathways, such as vasodilating drugs.