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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.

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Department of Chemical Engineering University of California, Los Angeles

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  1. 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

  2. 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

  3. 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

  4. (2) (1) (4) (3) Barriers for NO Uptake in the Blood

  5. 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

  6. 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

  7. 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

  8. 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

  9. Mathematical Modeling of NO Transport • Governing Equations: • Surrounding tissue (Abluminal region): • Vessel wall (Endothelium): • Vessel interior (lumen):

  10. Mathematical Modeling of NO Transport • Boundary Conditions: • Radial direction: • Azimuthal direction • Model parameters from experiments

  11. 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

  12. Simulations of Continuum Model • NO distribution in blood vessel and surrounding tissue

  13. Simulations of Continuum Model Radial variations of mean NO concentration

  14. Abluminal region Extra-cellular space Intracellular space Endothelium Effect of Red Blood Cells • Hemoglobin “packaged” inside permeable RBCs • Inter-cell diffusion (boundary layer)

  15. 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

  16. Simulations of Basic Particulate Model Radial variations of mean NO concentration for homogeneous & particulate models

  17. Abluminal region Extra-cellular space Intracellular space Endothelium Effect of RBC Membrane Permeability

  18. Simulations of Particulate Model+Membrane Radial variations of NO concentration for homogeneous, particulate & particulate+RBC membrane models

  19. Simulations of Full Particulate Model NO concentration profiles for homogeneous, particulate, particulate+membrane, &full particulate models

  20. Quantifying NO Transport Barriers • Computation of mass transfer resistance

  21. 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.

  22. 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

  23. 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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