Download Computational Modeling and Simulation of Nitric

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
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
Vessel wall
Barriers for NO Uptake in the Blood
(1)
(4)
(2)
(3)
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
Geometry of Blood Vessel
Abluminal region
(smooth muscle)
Blood vessel
lumen
R
R+e
Endothelium
(NO production)
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):
•
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
Spatially uniform NO-Hb reaction rate in vessel
Simulations of Continuum Model
•
NO distribution in blood vessel and surrounding tissue
Simulations of Continuum Model
Radial variations of mean NO concentration
Effect of Red Blood Cells
•
Hemoglobin “packaged” inside permeable RBCs
Inter-cell diffusion (boundary layer)
Abluminal region
Extra-cellular space
Intracellular space
Endothelium
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
Extra-cellular space
Intracellular space
Endothelium
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.
RBC membrane
Extracellular diffusion
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
45%
25%
15%
Blood hematocrit
5%
45%
25%
15%
Blood hematocrit
5%
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
Stationary
RBC
Flow