Microvascular Networks Jeremy Flannery Supervisor Dr Dan Goldman Department of Medical Biophysics The University of Western Ontario April 6 2010 Introduction Properties of Arterioles Extend from arteries and lead to capillaries ID: 927358
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Slide1
Heterogeneity of Oxygen Saturation in Microvascular Networks
Jeremy Flannery
Supervisor: Dr. Dan Goldman
Department of Medical Biophysics
The University of Western Ontario
April 6, 2010
Slide2Introduction
Properties of Arterioles
Extend from arteries and lead to capillaries
Diameters of about 100-10 μmSmooth muscle (SM) surroundsMany levels of bifurcation and branching: networks
Arteriole
Venule
Capillary
Function of Arterioles
Control vascular resistance through SM contraction and dilation
Allow blood flow into capillaries
Can allow for oxygen exchange
Slide3Background
Blood components
Plasma ~55% (accumulates on edges of vessel)
Red blood cells (RBC) ~44% (accumulates in centre of vessel)White blood cells and platelets ~1-2%
Plasma and RBC accumulation
Plasma SkimmingSaturation Bifurcation Effect
Slide4Background
Plasma Skimming Effect
Alters hematocrit at bifurcations when flow distribution is asymmetric (
Empirical Bifurcation Law)Leads to lowered apparent hematocrit at network exit
Blood Flow Fraction vs. Red Cell Flow Fraction in Daughter Vessel
Slide5Background
Saturation Bifurcation Effect :
Caused by diffusive oxygen losses from outer RBCs
Creates radial gradients in oxygen saturation within arterioles
low saturation
RBCs
near wall
high saturationRBCs near centre
high hematocrit
& oxygen saturationlow hematocrit& oxygen saturation
Slide6Objectives
To create an accurate theoretical model for oxygen distribution in
in vivo
microvascular networksInvestigate the effects of property alterations on oxygen saturation heterogeneityAnalyse hematocrit and oxygen saturations at lower levels of vessel bifurcationUse known biological properties to explain experimentally observed decrease in oxygen saturation at the capillary level
Slide7MATLAB Theoretical Model
Arteriolar network with 4 levels of bifurcations
Symmetric diameters at each bifurcation
Variable relative blood flow at each bifurcationConserve blood flow, RBC flow, oxygen flow at bifurcations
Set blood flow division at each bifurcationDetermine RBC division by empirical bifurcation law
Calculate oxygen saturation division
Slide8Methods
Vessel flow profiles in daughter vessels
Fluid speed
Red blood cell (hematocrit)Oxygen saturation
Solve for constants so, h
o, and uo
using conservation of flow
Slide9Conservation Laws
Conservation of volume flow:
Conservation of RBC flow:
Conservation of oxygen flow:
Slide10Methods Continued
Determine ‘a’ value for flow division
Find relationship between flow distribution as function of ‘a’
Extrapolate to find ‘a’ for given fractional distribution of flow at each bifurcation
Slide11Methods Continued
Determine ‘b’ RBC exponential at each bifurcation
Find relationship between RBC flow fraction for each daughter vessel as function of ‘b’
Extrapolate to find ‘b’ based on calculated RBC flow fraction
Slide12Results
Slide13Results
Increased heterogeneity of saturation at lower levels of arteriolar network
Values greater than original 0.35 occur
Slide14Results
Increased heterogeneity of saturation at lower levels of arteriolar network
Values greater than original 0.7 occur
Slide15Results
Q factor
Mean
d
ischarge hematocrit
at level 4
Mean
oxygen saturation at level 4
0.5
0.35
0.7
0.4
0.3423
0.6828
0.25
0.3004
0.5902
Increasing difference in flow between daughter vessels decreases average hematocrit and oxygen saturation
Apparent loss of hematocrit and oxygen saturation from initial values
Slide16Discussion
Heterogeneity in hematocrit due to:
Plasma skimming effect
Heterogeneity in oxygen saturation mainly due to:Saturation bifurcation effect Plasma skimmingInaccuracies of model
Flow speed and oxygen saturation quadratic distributionsZero oxygen saturation at walls of vessels
No oxygen loss by diffusion along networkAssumed diameter symmetry at bifurcations
Constant flow distributions at each bifurcation
Slide17Conclusion
Model showed:
Heterogeneity in hematocrit and saturation levels
Apparent loss of saturation and hematocritModel demonstrates and explains:Saturation bifurcation effectRole of plasma skimming
Pre-capillary loss of oxygen saturation and hematocrit not only due to diffusion through vessel walls
Slide18Acknowledgments
Dr. Dan Goldman- Supervisor
Dr. Chris Ellis- Originator of saturation bifurcation idea
Slide19Questions?