Posts Tagged ‘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.


Chen (2011) :

Mashour and Broock, Brain Res., 1999:

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

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

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

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

Mitochondrial Damage and Repair under Oxidative Stress

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

Nitric Oxide and Immune Responses: Part 2

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

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

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

Statins’ Nonlipid Effects on Vascular Endothelium through eNOS Activation

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

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.

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.

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

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



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Author and Reporter: Anamika Sarkar, Ph.D.

Today, the gold standard treatment for cancer is still chemo therapy or radiation therapy. Drugs are administered to treat patients with different doses, frequencies and combinations. It is recognized that the side effects of all these therapies lead to DNA damage responses (DDR) and their subsequent signaling alterations resulting in cellular functions. Moreover, it is well known that DDR is responsible for complex cross talks and feedback of signaling pathways for progrowth and apoptosis within intracellular as well as extracellular networks (in tissues).

Optimal combinations of drugs in respect of doses or frequencies or order of treatments of different drugs have been recognized as a powerful method of treatment of complex diseases. However, executing experiments of multiple possible combinations of drugs and cell lines can easily lead to very costly proposition. Lee in their paper published in Cell (2012), titled “Sequential Application of Anticancer Drugs Enhances Cell Death by Rewiring Apoptotic Signaling Networks”, reported from experimental results that when triple negative breast cancer (TNBC) cells are treated, with a combination of drugs  – erlotinib, which is an EGFR inhibitor, at least 4 hours before of another drug, doxorubicin – the cells show higher apoptotic (cell death) responses. Other forms of treatments like, single administration of the drugs or treating the cells together with two drugs at same time, did not show any increased levels of apoptosis in TNBC cells.

They complemented their understanding of reason behind such unique behavior of TNBC cells, when exposed to time -stagger treatment of drugs, with systems level modeling. They used quantitative analysis of high throughput reverse-phase protein microarrays and quantitative western blotting of experiments. They chose to measure activation states of 35 signaling proteins at 12 time points following exposure to ertolinib and doxorubicin individually and in combinations. The authors used PLS (Partial Least Square) and PCA (Principle Component Analysis) methods for predictive analysis from data driven model.

They report from their systems level analysis that time – stagger treatment of TNBC with two drugs ertolinib and doxorubicin activate Caspase 8, a key apoptotic signaling component, which remains absent in other combinations of treatments of drugs. They hypothesized that early treatment of ertolinib, inhibits EGFR responses, which increases levels of activated Caspase 8 and gets amplified after getting exposed to the second drug doxorubicin.

Combination therapy in treating complicated diseases like cancer has many importance in making the dose and treatment efficient. However, due to complex nature of signaling pathways, it poses increasing amount of challenges. Lee et. al., address some of those challenges by bringing in synergistic collaborations among different fields – experiments and mathematical modeling, which is the future of drug development.


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