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.