Computational Model of a Capillary: The effect of geometry on hemoglobin

measurements

Eugene JohMedical Biophysics

6-Week ProjectSupervisor: Dr. Dan Goldman

Introduction

• Microvasculature– Capillary dimensions– Site of molecule exchange– Complex geometry (depending on tissue type)

Background

• Hemoglobin– Iron containing, multi-subunit protein– Two general states:• Oxygenated (HbO2)• Deoxygenated (Hb)

– Main role in oxygen transport

Department of Biochemistry, UWO

Approach

• Dual Wavelength Videodensitometric Method– Absorbance (Optical Density, OD)• Beer-Lambert’s Law

– Oxygen dependent (431nm) & Isosbestic (420nm) • Ellsworth, Pittman, Ellis (1987)

Approach

• Oxygen Saturation (SO2)– S = m(OD431/OD420)+b• m and b are constants dependent on

– Extinction Coefficients• Values determined from known Hb solutions

Objectives

• Create a computational model that accurately estimates the HbO2 saturation of a single capillary from optical density measurements at two wavelengths in a specific volume of tissue– Investigate the application of multiple capillaries to the

model– Specifically to investigate the effect of stacked capillary

geometry on the sensitivity of estimating HbO2 saturation

MATLAB Model

• Primary model– Single capillary inside a volume of tissue– OD calculated with light scattering = 0– Linear saturation gradient to determine a proper

mean saturation– Extinction Coefficients optimized based on linear

saturation gradient

Methods

• From primary model, multiple capillaries added at different locations– Linear saturation gradient used to check mean

saturation calculation• Specific geometries arranged in the model– Add calculation of saturation directly dependent

on the intensity ratio– Determine an effect on finite sensitivity for

different geometries and cut-off

Results: 2 Capillaries

Cut-off: -9

Results: 2 Capillaries

Cut-off: -17

Results: 3 Capillaries

Cut-off: -9

Results: 3 Capillaries

Cut-off: -25

Results: 3 Capillaries

Cut-off: -30

Results: 3 Capillaries

Cut-off: -30

Discussion

• Stacked geometry directly causes an increase in error at smaller cut-offs

• Heterogeneity of the capillaries’ properties also increases the error in estimating the saturation

• Error due to method of data acquisition• Inaccuracies of Model– Assumptions of ideal flow and distribution of Hb– Parallel arrangements and symmetry– Saturation gradient being linear

Conclusion

• Specific geometries and heterogeneity of capillaries directly increases the error in estimating the saturation of the specific volume of tissue

Questions?