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Differential Distribution of Nitric Oxide – A 3-D Mathematical Model

Author and Reporter: Anamika Sarkar, Ph.D.

Among many important roles of Nitric oxide (NO), one of the key actions is to act as a vasodilator and maintain cardiovascular health. Induction of NO is regulated by signals in tissue as well as endothelium.

Importance of NO has been nicely reviewed in the article  “Discovery of NO and its effects of vascular biology”. Other articles which are good readings for the importance of NO are  – a) regulation of glycolysis b) NO in cardiovascular disease c) NO and Immune responses Part I and Part II d) NO signaling pathways (Also, please see Source for more articles on NO and its significance).

The rate of production of NO has been established to be dependent on Wall Shear Stress (WSS) (Mashour and Broock, Brain Res., 1999) . Many mathematical models have been developed as 2D diffusion models to predict distribution of NO transport in single vessels, eg. arterioles (Please see Sources for references ).

Chen et. al. (Med. Biol. Eng. Comp., 2011) developed a 3-D model consisting of two branched arterioles and nine capillaries surrounding the vessels. Their model not only takes into account of the 3-D volume, but also branching effects on blood flow (Please see Fig 1 and Fig 2 from Chen et. al. 2011 ).

Fig. 1 Blood phase separation with vascular branching. RBC
fractional flow in daughter branch alpha is not necessarily equal
to that in branch beta

The mathematical model considers dynamic characteristics related to blood flow, blood vessel structures and transport mechanism in the wall. The authors have considered effects of branching and ratio of diameters between blood vessels of parent and children to determine the fractional blood flow which gets distributed in the network. These branching effects of the vessels will also affect the blood volume or RBC (Red Blood Cell), hence NO consumption in the blood. Parameters in the model are either obtained or fitted with experimental results from literature. Their model assumes a linear relationship of NO production with wall shear stress which in turn will be regulated by blood flow determined by branching characteristics of blood vessels. Moreover, the mathematical model includes transport of NO through the blood vessels in the tissue (in the defined volume of the model) as diffusion model,. The model was solved using Finite Elements method using the software COMSOL.

Their model results show that wall shear stress changes depending upon the distribution of RBC in the microcirculations of blood vessels, which leads to differential production of NO along the vascular network. Levels of NO at vascular walls can be less in branches which receive more blood flow, due to the balance between higher consumption of NO by RBC and production of NO due to high wall stress.  Their 3-D simulations showed the importance of capillaries such that NO can be concentrated in tissues far away in distance from arterioles facilitating much controlled NO regulation.

Though, the 3-D model developed by Chen et. al., (2011) is an idealized mathematical model of blood flow with production and consumption of NO, depending upon WSS, yet it shows importance of structure of blood vessels in distributions of NO in vessels and tissues. Such a model with proper extension to larger network can give more insights into differential distributions of NO as a function of blood flow and wall shear stress. As nano-medicine become sophisticated in years to come, information of distribution of NO in tissues and blood vessels can help the medicine to be more targeted.

Sources:

Chen et.al. (2011) : http://www.ncbi.nlm.nih.gov/pubmed/21431938

Mashour and Broock, Brain Res., 1999: http://www.ncbi.nlm.nih.gov/pubmed?term=10526117

Mathematical Modes of NO Distribution in 2-D

Other research on Nitric Oxide and Vascular Biology on this Scientific Web Site include the following:

Nitric Oxide and Immune Responses: Part 1

Curator and Reporter: Aviral Vatsa, 10/18/2012

http://pharmaceuticalintelligence.com/2012/10/18/nitric-oxide-and-immune-responses-part-1/

Clinical Trials Results for Endothelin System: Pathophysiological role in Chronic Heart Failure, Acute Coronary Syndromes and MI – Marker of Disease Severity or Genetic Determination?

Curator: Aviva Lev-Ari, 10/19/2012

http://pharmaceuticalintelligence.com/2012/10/19/clinical-trials-results-for-endothelin-system-pathophysiological-role-in-chronic-heart-failure-acute-coronary-syndromes-and-mi-marker-of-disease-severity-or-genetic-determination/

Nitric Oxide and Sepsis, Hemodynamic Collapse, and the Search for Therapeutic Options

Curator and Reporter: Larry Bernstein, MD, 10/20/2012

http://pharmaceuticalintelligence.com/2012/10/20/nitric-oxide-and-sepsis-hemodynamic-collapse-and-the-search-for-therapeutic-options/

Mitochondrial Damage and Repair under Oxidative Stress

Curator: Larry H Bernstein, MD, FCAP, 10/28/2012

http://pharmaceuticalintelligence.com/2012/10/28/mitochondrial-damage-and-repair-under-oxidative-stress/

Nitric Oxide and Immune Responses: Part 2

Curator: Aviral Vatsa, PhD, MBBS, 10/28/2012

http://pharmaceuticalintelligence.com/2012/10/28/nitric-oxide-and-immune-responses-part-2/

Differential Distribution of Nitric Oxide – A 3-D Mathematical Model

Author: Anamika Sarkar, PhD, 10/28/2012

http://pharmaceuticalintelligence.com/2012/10/28/differential-distribution-of-nitric-oxide-a-3-d-mathematical-model/

Statins’ Nonlipid Effects on Vascular Endothelium through eNOS Activation

Curator, EAW: Larry Bernstein, 10/8/2012

http://pharmaceuticalintelligence.com/2012/10/08/statins-nonlipid-effects-on-vascular-endothelium-through-enos-activation/

Nitric Oxide Nutritional remedies for hypertension and atherosclerosis. It’s 12 am: do you know where your electrons are?

Author and Reporter: Meg Baker, 10/7/2012.

http://pharmaceuticalintelligence.com/2012/10/07/no-nutritional-remedies-for-hypertension-and-atherosclerosis-its-12-am-do-you-know-where-your-electrons-are/

Inhibition of ET-1, ETA and ETA-ETB, Induction of NO production, stimulation of eNOS and Treatment Regime with PPAR-gamma agonists (TZD): cEPCs Endogenous Augmentation for Cardiovascular Risk Reduction – A Bibliography

Curator: Aviva Lev-Ari, 10/4/2012.

http://pharmaceuticalintelligence.com/2012/10/04/inhibition-of-et-1-eta-and-eta-etb-induction-of-no-production-and-stimulation-of-enos-and-treatment-regime-with-ppar-gamma-agonists-tzd-cepcs-endogenous-augmentation-for-cardiovascular-risk-reduc/

Coronary Artery Disease – Medical Devices Solutions: From First-In-Man Stent Implantation, via Medical Ethical Dilemmas to Drug Eluting Stents August 13, 2012

Author: Aviva Lev-Ari, PhD, RN, 8/13/2012

http://pharmaceuticalintelligence.com/2012/08/13/coronary-artery-disease-medical-devices-solutions-from-first-in-man-stent-implantation-via-medical-ethical-dilemmas-to-drug-eluting-stents/

Vascular Medicine and Biology: CLASSIFICATION OF FAST ACTING THERAPY FOR PATIENTS AT HIGH RISK FOR MACROVASCULAR EVENTS Macrovascular Disease – Therapeutic Potential of cEPCs

Curator; Aviva Lev-Ari, PhD, RN, 8/24/2012

http://pharmaceuticalintelligence.com/2012/08/24/vascular-medicine-and-biology-classification-of-fast-acting-therapy-for-patients-at-high-risk-for-macrovascular-events-macrovascular-disease-therapeutic-potential-of-cepcs/

Curated/reported by : Aviral Vatsa PhD, MBBS

Based on : S Moncada et al

It was in 1980 that Furchgott & Zawadzki first described endothelium- dependent relaxation of the blood vessels by acetylcholine. Further studies in 1984 revealed that other factors such as bradykinin, histamine and 5-hydroxytryptamine release endothelium derived relaxing factor (EDRF), which can modulate vessel tone. EDRF was shown to stimulate soluble guanylate cyclase and was inhibited by haemoglobin. In 1986 it was demonstrated that superoxide (O2) anions mediated EDRF inactivation and that the inhibitors of EDRF generated superoxide (O2) anions in solution as a mean to inhibit EDRF. It was later established that all compounds that inhibit EDRF have one property in common, redox activity, which accounted for their inhibitory action on EDRF. One exception was haemoglobin, which inactivates EDRF by binding to it. In 1987 Furchgott proposed that EDRF might be nitric oxide (NO) based on a study of the transient relaxations of endothelium-denuded rings of rabbit aorta to ‘acidified’ inorganic nitrite (NO) solutions and the observations that superoxide dismutase (SOD, which removes O2) protected EDRF. Till then NO was not known to be produced in mammalian cells. In 1988 Palmer et al could detect NO production both biologically and chemically by chemiluminescence. The following year in 1989 the enzyme responsible for NO production, NO synthase, was discovered and L-arginine:NO pathway was proposed.

Roles of L-arginine:NO pathway

By 1987 it was proposed that NO is generated in tissues other than endothelium. Hibbs et al and Marletta et al proposed that NO was generated by macrophages. Moreover release of EDRF was demonstrated in cerebellar cells following activation with N-methyl-D- aspartate (NMDA ). Both noradrenergic and cholinergic responses are ‘controlled’ by the nitrergic system so that the release of NO (e.g., during electrical field stimulation) counteracts and dominates the response to the noradrenergic or cholinergic stimulus (Cellek & Moncada, 1997). Mechanism of penile erection was unveiled by the studies on nitrergic neurotransmission that led to therapeutic intervention. Selective damage of nitrergic nerves in disease states was proposed as a potent mechanism of pathophysiology. Broadly three areas of research based on three isoforms of NOS came into being;

• cardiovascular
• nervous
• immunology

Identification of NG-monomethyl-L-arginine (L-NMMA) as an inhibitor of the synthesis of NO lay the basis of future research into investigating the role of NO in biological systems. In 1989 it was demonstrated that intravenous infusion of L-NMMA resulted in increase in blood pressure that was reversible by infusing L-arginine. NO was thus implicated in constantly maintaining blood vessel tone. eNOS knockout studies showed a hypertensive phenotypes in the animal models and over expression of eNOS led to lowering of the blood pressure. Furthermore, eNOS activation was attributed to phosphorylation of a specific tyrosine residue in the enzyme.

NO and Mitochondria

http://pharmaceuticalintelligence.com/2012/09/16/nitric-oxide-has-a-ubiquitous-role-in-the-regulation-of-glycolysis-with-a-concomitant-influence-on-mitochondrial-function/

NO reacts with some of the complexes of the respiratory chain, and inhibits mitochondrial respiration – this is a well accepted notion. Initially it was believed that the target for NO was soluble guanylate cyclase, which in vasculature would lead to elevation of cGMP that eventually results in NO mediated vasodilatation and platelet aggregation inhibition. In 1994, another potential target, cytochrome c oxidase, for inhibitory effects of NO was discovered. This was a reversible effect, in competition with oxygen concentrations. Increases in NO production were also shown to inhibit cellular respiration irreversibly by selectively inhibiting complex I . Hence in 2002 it was proposed that this might be a mechanism through which cell pathology was initiated in certain conditions. Furthermore, NO was proposed to be implicated in the activation of the grp78-dependent stress response , via modulating calcium-related interaction between mitochondria and endoplasmic reticulum . This host defence mechanism might also have role in vasculature. Further evidence was provided in 2003 to link the role of NO in mitochondrogenesis and thus indicating that NO might be involved in the regulation of the balance between glycolysis and oxidative phosphorylation in cells.

NO and Pathophysiology

Lack of NO: By 2000, NO was established as a haemostatic regulator in the vasculature. Its absence was implicated in pathological states such as hypertension and vasospasm. These pathophysiological states share a common beginning of endothelial dysfunction, which has low NO production as one of its characterstic features. This dysfunction has been observed prior to the appearance of cardiovascular disease in predisposed subjects with family history of essential hypertension and atherosclerosis. The most likely mechanism for endothelial dysfunction is that of a reduced bioavailability of NO . The mechanism of this aspect is discussed elsewhere on this site. Protection against reduction of NO bio-availability in the vasculature is a vital therapeutic target and is extensively explored. This can be achieved by the use of antioxidants and/or augmentation of eNOS expression. In 2003 statins were shown to increase the production of endothelial NO in endothelial cell cultures and in animals by the reduction of oxidative stress or by increasing the coupling of the eNOS. It was way back in 1994 that oestrogen was shown to increase both the activity and expression of eNOS. In addition, more recently in 2003, oestrogen was shown to reduce the breakdown of available NO.

Excess of NO: In 2000 it was shown that NO produced from iNOS in vasculature is involved in extensive vasodilatation in septic shock. Later it was demonstrated that inhibition of mitochondrial respiration is an important component of the NO-induced tissue damage. This inhibition of respiration, which is initially NO-dependent and reversible, becomes persistent with time as a result of oxidative stress . Such metabolic hypoxic states where in tissues cannot utilise available oxygen due to NO, could also contribute to other inflammatory and degenerative conditions. An obvious therapeutic target for reducing NO production in such conditions would be L-NMMA. L-NMM was tested in a clinical trial for septic shock in 2004. The results were however disappointing probably due to the blanket reduction in NO production from other NOS enzymes there by having deleterious effects on the treatment group. More specific inhibitors for NOS forms are being investigated for in different disease states.

In conclusion, the L-arginine: NO pathway has had a major impact in many areas of research, specially vascular biology. A lot has been understood about this pathway and its interactions, therapeutic targets are being aggressively investigated, but further investigations are required to delineate further the role of NO in human health and disease.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1760731/?tool=pubmed

Nitric Oxide and Platelet Aggregation

Inhaled NO in Pulmonary Artery Hypertension and Right Sided Heart Failure

Cardiovascular Disease (CVD) and the Role of agent alternatives in endothelial Nitric Oxide Synthase (eNOS) Activation and Nitric Oxide Production

Nitric Oxide in bone metabolism

Nitric oxide and signalling pathways

Rationale of NO use in hypertension and heart failure