Oximeter
What It DoesHow It Works
Dr. Frank Walmsley
Oximeter - Use
Used in hospitals and surgery centers
To measure percent oxygen in the blood
And pulse rate
Oximeter - UseCommon type clips to finger.
Which way is better?
Oximeter – OperationHow Does It Work?
To answer that question, we need to know what’s inside.
Contains two diodes one with red light at 660 nm (visible) one with near infrared light at 940 nm
(invisible)
Oximeter - OperationThe red light at 660 nm (with a correction) measures
the amount of hemoglobin (Hb) in the blood.The infrared light at 940 nm (with a correction)
measures the amount of oxyhemoglobin (HbO2) in the blood.
The amount of O2 is the same as the amount of oxyhemoglobin.
The hemoglobin contains no O2.
Percent O2 is [HbO2]/([HbO2]+[Hb]) x 100
Oximeter - Operation
The diode light must reach the blood vessels unimpeded.
Some fingernail polish will interfere.If so, put the oximeter on so that the light does
not go through the fingernail.
Light Intensity
Incident light (I0) passes through a solution. Not all the light exits from the solution (It).
Light Transmittanceand Absorbance
It/I0 = T (transmittance)
100 x T = %T (percent transmittance)How much of the incident light goes through.
Light Transmittanceand Absorbance
A = -log10(T)
A is absorbance (and has no units)
How do we get concentrations?
Oximeter - CalculationsCoke Zero® solutions at different concentrations.Stock solution: 50 mL diluted to 250 mL
Left to right (1) Stock; (2) 75%; (3) 50%; (4) 25%Absorbance increases with increasing
concentration
Oximeter - Calculations
How does absorbance increase with concentration?
Simplest*: directlyA ∝ c*Occam’s Razor
Oximeter - CalculationsCoke Zero® solution in different amounts.
25 mL 50 mL 75 mL 100 mL 11 mm 22 mm 33 mm 44 mmAbsorbance increases with path length
Oximeter - Rabbit
We see this in ordinary situations (if we look)
Oximeter – Rose Wine
Oximeter - Calculations
How does absorbance increase with path length?
More light is absorbed as length increases.Simplest*: directlyA ∝ l*Occam’s Razor
Oximeter - Calculations
Expressed in Beer’s LawA ∝ l * c where l is path length and c is concentration
How do you make this an equality?
Oximeter - Calculations
Answer:Add a proportionality constantA = a * l * c
How do we know this is correct?GET DATA!
Oximeter - Calculations
Plot of manganese(II) concentration vs. A in an atomic absorption experiment.
Oximeter - Calculations
Plot of zinc(II) concentrations vs. A in an atomic absorption experiment. Why not linear?
Oximeter - Calculations
Eliminate last point – Absorbances “less than 1”
Oximeter - CalculationsHow do we get the concentrations?Beer’s Law: A = a * l * c
or sometimes written A = ε * l * cA = absorbance: amount of light absorbed at a given
wavelengthε = proportionality constant called absorptivity; if
concentration in mol/L, called molar absorptivity (formerly called extinction coefficient)
l = length of material light passes through usually in cmc = concentration
THUS: concentration is directly proportional to absorbance (A) at constant path length
Oximeter - Calculations
Measure A, calculate cAt 660 nm, ε for Hb = 3196 L/(mol cm)
ε for HbO2 = 320 L/(mol cm)At 940 nm, ε for Hb = 693 L/(mol cm) ε for HbO2 = 1214 L/(mol cm)l is a constant, assumed to be 1 cm (see the
units of ε)THUS c = A/(ε * l)
↓660 nm
↓940 nm
Oximeter - Calculations
NoteAt 660 nm, ε for HbO2 is about 10% of ε for Hb:
320 vs 3196At 940 nm, ε for HbO2 is not much more than ε
for Hb: 1214 vs 693
Oximeter - CalculationsHowever,A at 940 nm definitely measures a combination of HbO2 and Hb.
This is shown visually in the spectra of the two substances.
Oximeter – CalculationsAssumption 1
If A660 for HbO2 is ignored:
(1)A660 = εHb660 * l x CHb
(2)A940 = AHb940 + AHbO2940
= εHb940 * l * CHb + εHbO2940 * l * CHbO2
Two equations, two unknowns: CHb and CHbO2
A660 and A940 are measured
The four absorptivities are constants as is l
Oximeter – CalculationsAssumption 1
Assume l = 1 cm*Put in values for the molar absorptivities(1)A660 = 3196 x cHb
(2)A940 = AHb940 + AHbO2940
= 693 x cHb + 1214 x cHbO2
Two equations, two unknowns.If A660 is measured to be 0.745 and A940 2.698,
solve for concentrations and percent O2.*Actually not true but will cancel out in the percent calculation.
Oximeter – CalculationsAssumption 1
cHb = A660/3196 = 0.000233
cHbO2 = (3196 * A940 - A660 * 693)/(3196 * 1214)
= 0.00209Total Hb – 0.00209 + 0.000233 = 0.00232%O2 = (0.00209/0.00232)*100 = 90.1
Oximeter – CalculationsNo Assumptions
At both wavelengthsAtotal = AHb + AHbO2
A660 = 3196 * cHb + 320 * cHbO2 = 0.745
A940 = 693 * cHb + 1214 * cHbO2 = 2.698
Two equations, two unknowns.
Oximeter – CalculationsNo Assumptions
On line:http://www.hellam.net/algebra/simul1.html
Oximeter – CalculationsNo Assumptions
Another:http://www.analyzemath.com/Calculators/Calculator_syst_eq.html
Oximeter – CalculationsNo Assumptions
Notice that the answers are not the same.
0.000011226 and 1.22688
The second one does not show the entire answer; farther down the numbers is E-5
So beware of web sites!
Oximeter – CalculationsNo Assumptions
The old fashioned way.A660 = 3196 * cHb + 320 * cHbO2 = 0.745
A940 = 693 * cHb + 1214 * cHbO2 = 2.698
By substitution!
Oximeter – CalculationsNo Assumptions
Another old fashioned way.A660 = 3196 * cHb + 320 * cHbO2 = 0.745
A940 = 693 * cHb + 1214 * cHbO2 = 2.698
Use Cramer’s RuleUse of matrixesThe Determinant is the 2 x 2 matrix from the x
and y coefficients.
2 x 2 Matrix
* *a b
M a d c bc d
Oximeter – CalculationsNo Assumptions
A660 = 3196 * cHb + 320 * cHbO2 = 0.745
A940 = 693 * cHb + 1214 * cHbO2 = 2.698
6
3196 3203196*1214 693*320
693 1214
3.658*10
D
Oximeter – CalculationsNo Assumptions
A660 = 3196 * cHb + 320 * cHbO2 = 0.745
A940 = 693 * cHb + 1214 * cHbO2 = 2.698
For the x matrix, substitute for x coefficients0.745 320
0.745*1214 2.698*3202.698 1214
41.0
xD
Oximeter – CalculationsNo Assumptions
A660 = 3196 * cHb + 320 * cHbO2 = 0.745
A940 = 693 * cHb + 1214 * cHbO2 = 2.698
For the y matrix, substitute for y coefficients3196 0.745
3196*2.698 693*0.745693 2.698
7929
yD
Oximeter – CalculationsNo Assumptions
Cramer’s Rule
56
36
3
2 3
41.01.121*10
3.658*10
79292.168*10
3.658*10
2.168*10% *100 99.5%
2.179*10
x
y
Dx
DD
yD
yO
x y
Another Beer’s Law
Extra
Why does an oximeter measure pulse rate?
Oxygen (correctly called dioxygen) is a gas and its concentration in water varies with the pressure. (Henry’s Law)
So the absorption measurements need to be made at the same pressure – at the same point in the pulse cycle.