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

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 Introduction

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 how can NO maintain its biological function ? Paradox: how can NO maintain its biological function ? Barriers for NO uptake NO Transport-Reactions in Blood Vessel wall

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

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

Abluminal region (smooth muscle) Endothelium (NO production) R R+  Physical Dimensions: R=50  m,  =2.5  m Geometry of Blood Vessel Blood vessel lumen

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 O 2 Modeling Assumptions

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

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

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) Overview of Simulation Results Model Complexity grows

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

Radial variations of mean NO concentration Simulations of Continuum Model

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

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

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

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

Computation of mass transfer resistance Quantifying NO Transport Barriers

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.

Acknowledgements 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 NSF and NIH Conclusions

EC Stationary Flow RBC Effect of Blood Flow Creates a cell-depleted zone near vessel wall (~2.5  m)