Modelling the Dependency of
Oxygen Saturation Levels in Tissue
on the Blood Flow of Capillary Units
Ryan Divigalpitiya
Supervisor: Dr. Dan Goldman
Department of Medical Biophysics
The University of Western Ontario
March 22, 2011
Tuesday, March 22, 2011
Introduction
Motivation
Broaden Our Understanding
- How O2 saturation varies in tissue
- Mechanisms and tissue properties that influence O2
saturation
Model Diseases that Impact O2 Saturation
- Predict Symptoms
- Reveal strategies for treatment & cures
Tuesday, March 22, 2011
Introduction
Background
Start with a Simple Case:
Healthy Tissue
Single Capillary
Tuesday, March 22, 2011
Introduction
Background
Start with a Simple Case:
Healthy Tissue
Single Capillary
Input
Tuesday, March 22, 2011
Algorithm
Output (O2)
Introduction
Background
Ellsworth ML, Pittman RN, Ellis CG. Measurement of Hemoglobin Oxygen Saturation in Capillaries. Am J
Physiol Heart Circ Physiol 252: H1031–H1040, 1987.
Tuesday, March 22, 2011
Introduction
Background
Ellsworth ML, Pittman RN, Ellis CG. Measurement of Hemoglobin Oxygen Saturation in Capillaries. Am J
Physiol Heart Circ Physiol 252: H1031–H1040, 1987.
Hemoglobin absorbs light at
specific wavelengths
Log(Io/IT) = Optical Density (OD)
Tuesday, March 22, 2011
Introduction
Background
Ellsworth ML, Pittman RN, Ellis CG. Measurement of Hemoglobin Oxygen Saturation in Capillaries. Am J
Physiol Heart Circ Physiol 252: H1031–H1040, 1987.
Hemoglobin absorbs light at
specific wavelengths
Log(Io/IT) = Optical Density (OD)
Tuesday, March 22, 2011
Tissue
Introduction
Background
Ellsworth ML, Pittman RN, Ellis CG. Measurement of Hemoglobin Oxygen Saturation in Capillaries. Am J
Physiol Heart Circ Physiol 252: H1031–H1040, 1987.
Hemoglobin absorbs light at
specific wavelengths
Log(Io/IT) = Optical Density (OD)
Io
Tissue
IT
Tuesday, March 22, 2011
Introduction
Background
Optical Density
(OD)
Tuesday, March 22, 2011
Correlated with
Oxygen Saturation
(O2 Sat.)
Introduction
Background
Optical Density
(OD)
Correlated with
Oxygen Saturation
(O2 Sat.)
O2 Saturation = - 1.56(OD431/OD420) + 1.78
Tuesday, March 22, 2011
Introduction
Background
Optical Density
(OD)
Correlated with
Oxygen Saturation
(O2 Sat.)
O2 Saturation = - 1.56(OD431/OD420) + 1.78
Model’s Algorithm Based on This Equation
Tuesday, March 22, 2011
Objective
To create a software computational model that
accurately predicts mean O2 tissue saturation based on
the Saturation Equation
Learn from constructing a simple model and
determine ways to make it more practical
Varying Hematocrit and Observing its Effect on
Finite Sensitivity
Tuesday, March 22, 2011
Methods
MATLAB
Image of Red Blood Cells taken from: http://www.fi.edu/learn/heart/blood/red.html, no copyright infringement intended, used for educational purposes only
Tuesday, March 22, 2011
Methods
MATLAB
1st Component - Geometry
- used MATLAB to construct a 3D matrix representing tissue
- define a cylinder representing the idealized capillary
Image of Red Blood Cells taken from: http://www.fi.edu/learn/heart/blood/red.html, no copyright infringement intended, used for educational purposes only
Tuesday, March 22, 2011
y
x
z
Methods
MATLAB
1st Component - Geometry
- used MATLAB to construct a 3D matrix representing tissue
- define a cylinder representing the idealized capillary
2nd Component - Tissue Properties
- simulate hemoglobin concentrations
- simulate hematocrit levels
- simulate decrease in saturation across capillary for testing
- neglected blood flow velocity for simplicity
Image of Red Blood Cells taken from: http://www.fi.edu/learn/heart/blood/red.html, no copyright infringement intended, used for educational purposes only
Tuesday, March 22, 2011
y
x
z
Methods
MATLAB
1st Component - Geometry
- used MATLAB to construct a 3D matrix representing tissue
- define a cylinder representing the idealized capillary
y
x
z
2nd Component - Tissue Properties
- simulate hemoglobin concentrations
- simulate hematocrit levels
- simulate decrease in saturation across capillary for testing
- neglected blood flow velocity for simplicity
3rd Component - Saturation Equation
- Incorporate Sat. Equation in a way that is used to predict
mean saturation of the modelled tissue
O2 Sat. = - 1.56(OD431/OD420) + 1.78
Image of Red Blood Cells taken from: http://www.fi.edu/learn/heart/blood/red.html, no copyright infringement intended, used for educational purposes only
Tuesday, March 22, 2011
Results
Contour Plots
Colour Bar In Units of Saturation Percentage
Tuesday, March 22, 2011
Results
Contour Plots
0.8
Capillary
Colour Bar In Units of Saturation Percentage
Tuesday, March 22, 2011
0.2
Results
Contour Plots
Should be 0.5
0.8
Capillary
Colour Bar In Units of Saturation Percentage
Tuesday, March 22, 2011
0.2
Results
Contour Plots
Should be 0.5
0.8
Capillary
Colour Bar In Units of Saturation Percentage
Tuesday, March 22, 2011
0.2
Results
Variation of Saturation Along Capillary
Colour Bar In Log Units
Tuesday, March 22, 2011
Results
Finite Sensitivity
Tuesday, March 22, 2011
Results
Finite Sensitivity
Tuesday, March 22, 2011
Results
Hematocrit Levels Influencing Finite Sensitivity
Hc = 0.3
Hc = 0.35
Hc = 0.45
Tuesday, March 22, 2011
Hc = 0.40
Hc = 0.50
Results
Hematocrit Levels Influencing Finite Sensitivity
Hc = 0.3
Hc = 0.35
Hc = 0.45
Tuesday, March 22, 2011
Hc = 0.40
Hc = 0.50
Discussion
Is this Basic Model Working?
- Predicted Mean Saturation = 0.5
- Finite Sensitivity Plots shows the sensitivity must be
higher for higher levels of hematocrit - this makes
sense: OD = Log(Io/Im) = Conc*dy*E
- This means we can use this model to predict what
the finite sensitivity of our measurement system
should be for certain levels of hematocrit
Tuesday, March 22, 2011
Discussion
Future Ideas: Improvement
What’s the Next Step?
Tuesday, March 22, 2011
Discussion
Future Ideas: Improvement
What’s the Next Step?
Simplification used: Linear Decrease in Saturation along Capillary
Tuesday, March 22, 2011
Discussion
Future Ideas: Improvement
What’s the Next Step?
Simplification used: Linear Decrease in Saturation along Capillary
How can someone determine the true function that
governs how saturation decreases over position?
Tuesday, March 22, 2011
@Z1
Z
@Z2
@Z3
@Z4
@Z5
Capillary
S = -1.56*(OD431/OD420)+1.78
Tuesday, March 22, 2011
@Z1
Io
@Z2
Io
@Z3
Io
@Z4
Io
@Z5
Io
Capillary
Z
I
S1
I
S2
I
S3
I
S4
I
S5
S = -1.56*(OD431/OD420)+1.78
Tuesday, March 22, 2011
@Z1
Io
@Z2
Io
@Z3
Io
@Z4
Io
@Z5
Io
Capillary
Z
I
S1
I
I
S2
S3
S4
I
S5
S = -1.56*(OD431/OD420)+1.78
Plot
Values
Tuesday, March 22, 2011
I
Z
S
Z1
Z2
Z3
Z4
Z5
S1
S2
S3
S4
S5
@Z1
Io
@Z2
Io
@Z3
Io
@Z4
Io
@Z5
Io
Capillary
Z
I
I
S1
I
S2
I
S3
S4
Plot
Values
Z
S
Z1
Z2
Z3
Z4
Z5
S1
S2
S3
S4
S5
Ask computer to apply a
best line of fit
X
X
X
Z
Tuesday, March 22, 2011
S5
S = -1.56*(OD431/OD420)+1.78
X
S
I
X
Computer will tell you
what the equation is:
Equation will be Saturation
as a function of Z:
S(Z)
Conclusion
- Model successfully predicts saturation based on Dr.
Ellis’s Saturation Equation
- Model shows that Higher levels of Hematocrit requires
Higher Finite Sensitivity
- Future Idea would derive an accurate function
describing the decrease in saturation which can then be
used in the model to improve its purpose
Tuesday, March 22, 2011
Thank you for your time
Tuesday, March 22, 2011
References
1. Daniel Goldman, Ryon M. Bateman, and Christopher G. Ellis, “Effect of sepsis on skeletal muscle
oxygen consumption and tissue oxygenation: interpreting capillary oxygen transport data using a
mathematical model”, Am J Physiol Heart Circ Physiol 287: H2535–H2544, 2004.
2. Mary L Ellsworth, Roland N. Pittman & Christopher G Ellis, “Measurement
of hemoglobin oxygen
saturation in capillaries”, 0363-6135/87 1.50 Copyright 1987 the American Physiological Society
Questions
Tuesday, March 22, 2011