Computational Modeling & Simulation of Nitric Oxide Transport-Reaction in the Blood
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Computational Modeling & Simulation of Nitric Oxide Transport-Reaction in the Blood. Nael H. El-Farra Panagiotis D. Christofides James C. Liao. Department of Chemical Engineering University of California, Los Angeles. 2003 AIChE Annual Meeting San Francisco, CA November 17, 2003.

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Computational Modeling & Simulation of Nitric Oxide Transport-Reaction in the Blood

Nael H. El-Farra

Panagiotis D. Christofides

James C. Liao

Department of Chemical Engineering

University of California, Los Angeles

2003 AIChE Annual Meeting

San Francisco, CA

November 17, 2003


Introduction

  • Nitric oxide (NO) : active free radical

    • Immune response

    • Neuronal signal transduction

    • Inhibition of platelet adhesion & aggregation

    • Regulation of vascular tone and permeability

  • Versatility as a biological signaling molecule

    • Molecule of the year (Science, 1993)

    • Nobel Prize (Dr. Ignarro, UCLA, 1998)

  • Need for fundamental understanding of NO regulation

    • Distributed modeling


Vessel wall

NO Transport-Reactions in Blood

  • Complex mechanism:

    • Release in blood vessel wall

    • Diffusion into surrounding tissue

      • Blood pressure regulation

    • Diffusion into vessel interior

      • Scavenging by hemoglobin

      • Trace amounts can abolish NO

  • Paradox: how can NO maintain its biological function ?

    • Barriers for NO uptake


(2)

(1)

(4)

(3)

Barriers for NO Uptake in the Blood


Previous Work on Modeling NO Transport

  • Homogenous models:

    • Blood treated as a continuum

      • e.g., Lancaster, 1994; Vaughn et al., 1998

  • Single-cell models:

    • Neglects inter-cellular diffusion

      • e.g., Vaughn et al., 2000; Liu et al., 2002

  • Survey of previous modeling works (Buerk, 2001)

  • Limitations:

    • Population of red blood cells (RBC) unaccounted for

    • Cannot quantify relative significance of barriers


Present Work

(El-Farra, Christofides, & Liao, Annals Biomed. Eng., 2003)

  • Objectives:

    • Develop a detailed multi-particle model to describe NO transport-reactions in the blood

    • Use the developed model to investigate sources for NO transport resistance

      • Boundary layer diffusion (RBC population)

      • RBC membrane permeability

      • Cell-free zone

    • Quantify barriers for NO uptake


Abluminal region (smooth muscle)

Blood vessel lumen

R

R+e

Endothelium (NO production)

Geometry of Blood Vessel

Physical Dimensions:

R=50 mm, e =2.5 mm


Modeling Assumptions

  • Steady-state behavior:

    • Small characteristic time for diffusion/reaction

      (~10 ms)

  • NO diffusivity independent of concentration or position

    • NO is dilute

  • Isotropic diffusion

  • Convective transport of NO negligible

    • Axial gradient small vs. length of region emitting NO

  • Hb is main source of NO consumption

    • Negligible reaction rates with O2


Mathematical Modeling of NO Transport

  • Governing Equations:

  • Surrounding tissue (Abluminal region):

  • Vessel wall (Endothelium):

  • Vessel interior (lumen):


Mathematical Modeling of NO Transport

  • Boundary Conditions:

    • Radial direction:

    • Azimuthal direction

    • Model parameters from experiments


Overview of Simulation Results

  • Continuum model (Basic scenario):

    • Spatially uniform NO-Hb reaction rate in vessel

  • Particulate model:

    • Barriers for NO uptake:

      • Red blood cells (infinitely permeable)

      • RBC membrane permeability

      • Cell-free zone

  • Transport resistance analysis

  • Numerical solutions thru finite-element algorithms

    • Adaptive mesh (finer mesh near boundaries)

Model Complexity grows


Simulations of Continuum Model

  • NO distribution in blood vessel and surrounding tissue


Simulations of Continuum Model

Radial variations of mean NO concentration


Abluminal region

Extra-cellular space

Intracellular space

Endothelium

Effect of Red Blood Cells

  • Hemoglobin “packaged” inside permeable RBCs

    • Inter-cell diffusion (boundary layer)


Simulations of Basic Particulate Model

  • NO distribution in blood vessel and surrounding tissue

  • Blood hematocrit determines number of cells

    • ~ 45-50% under normal physiological conditions


Simulations of Basic Particulate Model

Radial variations of mean NO concentration for homogeneous & particulate models


Abluminal region

Extra-cellular space

Intracellular space

Endothelium

Effect of RBC Membrane Permeability


Simulations of Particulate Model+Membrane

Radial variations of NO concentration for homogeneous, particulate & particulate+RBC membrane models


Simulations of Full Particulate Model

NO concentration profiles for homogeneous, particulate, particulate+membrane, &full particulate models


Quantifying NO Transport Barriers

  • Computation of mass transfer resistance


Relative Significance of Transport Barriers

  • Fractional resistance is a strong function of blood hematocrit:

    • Membrane resistance dominant at high Hct.

    • Extra-cellular diffusion dominant at low Hct.


Conclusions

  • Mathematical modeling of NO diffusion-reaction in blood

  • Diffusional limitations of NO transport:

    • Population of red blood cells

    • RBC membrane permeability

    • Cell free zone

  • Relative significance of resistances depends on Hct.

  • Practical implications:

    • Encapsulation of Hb in design of blood substitutes

  • Acknowledgements

    • NSF and NIH


    Effect of Blood Flow

    • Creates a cell-depleted zone near vessel wall (~2.5 mm)

    EC

    EC

    EC

    EC

    RBC

    RBC

    Stationary

    Flow


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