1. Oximeter What It Does How It Works Dr. Frank Walmsley

2. Oximeter - Use Used in hospitals and surgery centers To measure percent oxygen in the blood And pulse rate

3. Oximeter - Use Common type clips to finger. Which way is better?

4. Oximeter – Operation How 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)

5. Oximeter - Operation The 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 (HbO 2 ) in the blood. The amount of O 2 is the same as the amount of oxyhemoglobin. The hemoglobin contains no O 2. Percent O 2 is [HbO 2 ]/([HbO 2 ]+[Hb]) x 100

6. 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.

7. Light Intensity Incident light (I 0 ) passes through a solution. Not all the light exits from the solution (I t ).

8. Light Transmittance and Absorbance I t /I 0 = T (transmittance) 100 x T = %T (percent transmittance) How much of the incident light goes through.

9. Light Transmittance and Absorbance A = -log 10 (T) A is absorbance (and has no units) How do we get concentrations?

10. Oximeter - Calculations Coke 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

11. Oximeter - Calculations How does absorbance increase with concentration? Simplest*: directly A ∝ c *Occam’s Razor

12. Oximeter - Calculations Coke Zero ® solution in different amounts. 25 mL 50 mL 75 mL 100 mL 11 mm 22 mm 33 mm 44 mm Absorbance increases with path length

13. Oximeter - Rabbit We see this in ordinary situations (if we look)

14. Oximeter – Rose Wine

15. Oximeter - Calculations How does absorbance increase with path length? More light is absorbed as length increases. Simplest*: directly A ∝ l *Occam’s Razor

16. Oximeter - Calculations Expressed in Beer’s Law A ∝ l * c where l is path length and c is concentration How do you make this an equality?

17. Oximeter - Calculations Answer: Add a proportionality constant A = a * l * c How do we know this is correct? GET DATA!

18. Oximeter - Calculations Plot of manganese(II) concentration vs. A in an atomic absorption experiment.

19. Oximeter - Calculations Plot of zinc(II) concentrations vs. A in an atomic absorption experiment. Why not linear?

20. Oximeter - Calculations Eliminate last point – Absorbances “less than 1”

21. Oximeter - Calculations How do we get the concentrations? Beer’s Law: A = a * l * c or sometimes written A = ε * l * c A = absorbance: amount of light absorbed at a given wavelength ε = 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 cm c = concentration THUS: concentration is directly proportional to absorbance (A) at constant path length

22. Oximeter - Calculations Measure A, calculate c At 660 nm, ε for Hb = 3196 L/(mol cm) ε for HbO 2 = 320 L/(mol cm) At 940 nm, ε for Hb = 693 L/(mol cm) ε for HbO 2 = 1214 L/(mol cm) l is a constant, assumed to be 1 cm (see the units of ε) THUS c = A/(ε * l )

23. ↓660 nm ↓940 nm

24. Oximeter - Calculations Note At 660 nm, ε for HbO 2 is about 10% of ε for Hb: 320 vs 3196 At 940 nm, ε for HbO 2 is not much more than ε for Hb: 1214 vs 693

25. Oximeter - Calculations However, A at 940 nm definitely measures a combination of HbO 2 and Hb. This is shown visually in the spectra of the two substances.

26. Oximeter – Calculations Assumption 1 If A 660 for HbO 2 is ignored: (1)A 660 = ε Hb660 * l x C Hb (2)A 940 = A Hb940 + A HbO2940 = ε Hb940 * l * C Hb + ε HbO2940 * l * C HbO2 Two equations, two unknowns: C Hb and C HbO2 A 660 and A 940 are measured The four absorptivities are constants as is l

27. Oximeter – Calculations Assumption 1 Assume l = 1 cm* Put in values for the molar absorptivities (1)A 660 = 3196 x c Hb (2)A 940 = A Hb940 + A HbO2940 = 693 x c Hb + 1214 x c HbO2 Two equations, two unknowns. If A 660 is measured to be 0.745 and A 940 2.698, solve for concentrations and percent O 2. *Actually not true but will cancel out in the percent calculation.

28. Oximeter – Calculations Assumption 1 c Hb = A 660 /3196 = 0.000233 c HbO2 = (3196 * A 940 - A 660 * 693)/(3196 * 1214) = 0.00209 Total Hb – 0.00209 + 0.000233 = 0.00232 %O 2 = (0.00209/0.00232)*100 = 90.1

29. Oximeter – Calculations No Assumptions At both wavelengths A total = A Hb + A HbO2 A 660 = 3196 * c Hb + 320 * c HbO2 = 0.745 A 940 = 693 * c Hb + 1214 * c HbO2 = 2.698 Two equations, two unknowns.

30. Oximeter – Calculations No Assumptions On line: http://www.hellam.net/algebra/simul1.html

31. Oximeter – Calculations No Assumptions Another: http://www.analyzemath.com/Calculators/Calculator_syst_eq.html

32. Oximeter – Calculations No 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!

33. Oximeter – Calculations No Assumptions The old fashioned way. A 660 = 3196 * c Hb + 320 * c HbO2 = 0.745 A 940 = 693 * c Hb + 1214 * c HbO2 = 2.698 By substitution!

34. Oximeter – Calculations No Assumptions Another old fashioned way. A 660 = 3196 * c Hb + 320 * c HbO2 = 0.745 A 940 = 693 * c Hb + 1214 * c HbO2 = 2.698 Use Cramer’s Rule Use of matrixes The Determinant is the 2 x 2 matrix from the x and y coefficients.

35. 2 x 2 Matrix

36. Oximeter – Calculations No Assumptions A 660 = 3196 * c Hb + 320 * c HbO2 = 0.745 A 940 = 693 * c Hb + 1214 * c HbO2 = 2.698

37. Oximeter – Calculations No Assumptions A 660 = 3196 * c Hb + 320 * c HbO2 = 0.745 A 940 = 693 * c Hb + 1214 * c HbO2 = 2.698 For the x matrix, substitute for x coefficients

38. Oximeter – Calculations No Assumptions A 660 = 3196 * c Hb + 320 * c HbO2 = 0.745 A 940 = 693 * c Hb + 1214 * c HbO2 = 2.698 For the y matrix, substitute for y coefficients

39. Oximeter – Calculations No Assumptions Cramer’s Rule

40. Another Beer’s Law

41. 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.