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

Introduction Properties of Arterioles Extend from arteries and lead to capillaries Diameters of about μm Smooth muscle (SM) surrounds Many 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

Background 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 Skimming Saturation Bifurcation Effect

Background 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

Background 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 saturation RBCs near centre high hematocrit & oxygen saturation low hematocrit & oxygen saturation

Objectives To create an accurate theoretical model for oxygen distribution in in vivo microvascular networks Investigate the effects of property alterations on oxygen saturation heterogeneity Analyse hematocrit and oxygen saturations at lower levels of vessel bifurcation Use known biological properties to explain experimentally observed decrease in oxygen saturation at the capillary level

MATLAB Theoretical Model Arteriolar network with 4 levels of bifurcations Symmetric diameters at each bifurcation Variable relative blood flow at each bifurcation Conserve blood flow, RBC flow, oxygen flow at bifurcations Set blood flow division at each bifurcation Determine RBC division by empirical bifurcation law Calculate oxygen saturation division

Methods Vessel flow profiles in daughter vessels Fluid speed Red blood cell (hematocrit) Oxygen saturation Solve for constants s o, h o, and u o using conservation of flow

Conservation Laws Conservation of volume flow: Conservation of RBC flow: Conservation of oxygen flow:

Methods 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

Methods 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

Results

Increased heterogeneity of saturation at lower levels of arteriolar network Values greater than original 0.35 occur

Results Increased heterogeneity of saturation at lower levels of arteriolar network Values greater than original 0.7 occur

Results Q factor Mean discharge hematocrit at level 4 Mean oxygen saturation at level Increasing difference in flow between daughter vessels decreases average hematocrit and oxygen saturation Apparent loss of hematocrit and oxygen saturation from initial values

Discussion Heterogeneity in hematocrit due to: Plasma skimming effect Heterogeneity in oxygen saturation mainly due to: Saturation bifurcation effect Plasma skimming Inaccuracies of model Flow speed and oxygen saturation quadratic distributions Zero oxygen saturation at walls of vessels No oxygen loss by diffusion along network Assumed diameter symmetry at bifurcations Constant flow distributions at each bifurcation

Conclusion Model showed: Heterogeneity in hematocrit and saturation levels Apparent loss of saturation and hematocrit Model demonstrates and explains: Saturation bifurcation effect Role of plasma skimming Pre-capillary loss of oxygen saturation and hematocrit not only due to diffusion through vessel walls

Acknowledgments Dr. Dan Goldman- Supervisor Dr. Chris Ellis- Originator of saturation bifurcation idea

Questions?