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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Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

(2)

(1)

(4)

(3)

Barriers for NO Uptake in the Blood


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

Mathematical Modeling of NO Transport

  • Governing Equations:

  • Surrounding tissue (Abluminal region):

  • Vessel wall (Endothelium):

  • Vessel interior (lumen):


Department of chemical engineering university of california los angeles

Mathematical Modeling of NO Transport

  • Boundary Conditions:

    • Radial direction:

    • Azimuthal direction

    • Model parameters from experiments


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

Simulations of Continuum Model

  • NO distribution in blood vessel and surrounding tissue


Department of chemical engineering university of california los angeles

Simulations of Continuum Model

Radial variations of mean NO concentration


Department of chemical engineering university of california los angeles

Abluminal region

Extra-cellular space

Intracellular space

Endothelium

Effect of Red Blood Cells

  • Hemoglobin “packaged” inside permeable RBCs

    • Inter-cell diffusion (boundary layer)


Department of chemical engineering university of california los angeles

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


Department of chemical engineering university of california los angeles

Simulations of Basic Particulate Model

Radial variations of mean NO concentration for homogeneous & particulate models


Department of chemical engineering university of california los angeles

Abluminal region

Extra-cellular space

Intracellular space

Endothelium

Effect of RBC Membrane Permeability


Department of chemical engineering university of california los angeles

Simulations of Particulate Model+Membrane

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


Department of chemical engineering university of california los angeles

Simulations of Full Particulate Model

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


Department of chemical engineering university of california los angeles

Quantifying NO Transport Barriers

  • Computation of mass transfer resistance


Department of chemical engineering university of california los angeles

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.


Department of chemical engineering university of california los angeles

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


    Department of chemical engineering university of california los angeles

    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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