1. Lecture 7 Part II Tissue optical properties (Absorption) Acknowledgement Slides on absorption spectroscopy based on Lecture prepared by Dr. Nimmi Ramanujam, University of Wisconsin at Madison

2. Tissue optical properties There are two main tissue optical properties which characterize light-tissue interaction and determine therapeutic or diagnostic outcome: –Absorption coefficient:  a (cm -1 )  a =  a *N a =A/L*ln10  a =atomic absorption cross section (cm 2 ) N a =# of absorbing molecules/unit volume (cm -3 ) A=Absorbance L=sample length –Scattering coefficient:  s (cm -1 )  s =  s *Ns  s =atomic scattering cross section (cm 2 ) N s =# of scattering molecules/unit volume (cm -3 ) Area  a = Q a Area  s = Q s Area Q a – absorption efficiency Q s – scattering efficiency

3. Population of Energy Levels At any finite T, molecules will be distributed among available E levels due to thermal agitation The exact distribution among energy levels will depend upon the temperature and separation between energy levels according to Boltzmann statistics k=1.38*10 -23 JK -1 (Boltzmann’s constant)  E = separation in energy level

4. Energy Levels Population of energy levels

5. Absorption Spectroscopy Population of energy levels Net absorption depends on the difference between the populations of the energy levels The more populated the ground state, the more intense the net absorption is Two factors that influence absorption are the energy level spacing and the temperature

6. Energy Levels UV Visible absorption spectroscopy involves transitions between electronic energy levels UV ~ 200-400nm Vis ~ 400-750nm For < 200nm (absorption by oxygen in air is significant) – vacuum UV

7. II. Absorption Spectroscopy Electron transition rules Energy is absorbed by transitions induced between different electronic energy states of a molecule Transition occurs only if there is an induced dipole moment Resonance condition; the frequency of radiation must be equal to the frequency of the dipole  E = hf where,  E = separation of energy states, h = Planck’s constant, f = frequency h=6.626x10 -34 m 2 kg/s

8. Absorption strength The transition probability from electronic state m to state n is given by: Where,  mn is the transition dipole moment and   is molar extinction coefficient at particular frequency, II. Absorption Spectroscopy

9. B. Franck Condon principle The time for an electronic transition is: t=1/ = /c ~ 10 -15 s (at 420 nm) Franck Condon principle: electronic transitions occur so rapidly that during the transition the nuclei are static Thus, all electronic transitions are vertical (internuclear distance doesn’t change)

10. Energy II. Absorption Spectroscopy B. Franck Condon principle Internuclear distance

11. II. Absorption Spectroscopy B. Spectral line widths Electronic transitions to different vibrational energy levels With enough of these transitions the absorption spectrum looks more like a smooth curve rather than a line

12. Absorption spectroscopy Lifetime broadening –A molecule spends only a short amount of time in its excited state, which defines the lifetime, , of the state. –If a molecule changes states at a rate of 1/ , then the energy levels become blurred and the corresponding spread in the energy levels around E is (Heisenberg uncertainty principle)  = 10 -12 s   0.08nm (for = 400nm)

13. Absorption spectroscopy Doppler broadening –With the thermal motion of the atoms, those atoms traveling toward the detector with a velocity v will have transition frequencies which differ from those of atoms at rest by the Doppler shift. –  o =frequency for atom at rest –m o =atomic mass http://www.walter-fendt.de/ph11e/dopplereff.htm

14. II. Absorption Spectroscopy C. Biological chromophores 1.The peptide bonds and amino acids in proteins The p electrons of the peptide group are delocalized over the carbon, nitrogen, and oxygen atoms. The n-  * transition is typically observed at 210-220 nm, while the main  -  * transition occurs at ~190 nm. Aromatic side chains contribute to absorption at > 230 nm 2. Purine and pyrimidine bases in nucleic acids and their derivatives 3. Highly conjugated double bond systems

15. III. Biological Chromophores Molecule  (nm)  (x10 -3 ) (cm 2.mol -1 ) Tryptophan280, 2195.6,47 Tyrosine274,222,1931.4,8,48 Phenylalanine257,206,1880.2,9.3,60 Histidine2115.9 Cystine2500.3 1. Amino acids

16. III. Biological Chromophores Tryptophan absorption is used as the basis for protein concentration measurements

17. III. Biological Chromophores Molecule  (nm)  (x10 -3 ) (cm 2.mol -1 ) Adenine260.513.4 Adenosine259.514.9 NADH340,2596.23, 14.4 NAD+2605.9, 18 FAD+450unknown 2. Bases and their derivatives

18. III. Biological Chromophores 3. Highly conjugated double bond systems Spectrum is often in the visible region (electrons less restricted, energy levels closer) Metal porphyrin ring system is mainly responsible for the color in heme proteins The most intense band is called the Soret band after its discoverer

19. 3. Hemoglobin Absorption Spectra Major absorption peaks around 400 and 540-580nm are due to  * transitions of the porphyrin ring The band in HbO 2 around 900 nm arises from charge transfer between the porphyrin protein and the Fe(II) atom

20. Beta carotene absorption spectrum Absorption due to  transitions

21. Melanin absorption eumelanin A black-to-dark-brown insoluble material found in human black hair and in the retina of the eye. pheomelanin A yellow-to-reddish-brown alkali-soluble material found in red hair and red feathers. A variety of low molecular weight pheomelanins are called "trichromes".

22. Tissue absorbers Therapeutic window: 600-900 nm region where not much absorption takes place

23. II.Absorption Spectroscopy D. Concentration of molecules Absorption depends on the number of molecules in which transitions are induced. Absorption spectra can be used quantitatively The effect of sample concentration on the absorption is the basis of most analytical applications

25. Molar absorption cross- section=  a *N A (N A is Avogadro’s number)

27. 1/log 10 (e)=2.303

28. Determining Concentrations (C) IoI Path length, L Absorbing sample of concentration C

29. II. Absorption Spectroscopy F. Instrumentation and measurement 1.Typical instrument 2.Experimental techniques

30. II. Absorption Spectroscopy Mono- chromator White Light S R Sample Chamber Electronics Detector BS M Chopper BS M I Io

31. Absorption Spectroscopy 2. Experimental technique a. What can be measured? b. Modes of measurement c. Parameters d. Base line e. Sample and reference measurements f. Considerations

32. II. Absorption Spectroscopy a. What can be measured? Absorbing, non-scattering samples Liquid samples contained in cuvettes

33. II. Absorption Spectroscopy b. Modes of measurement Absorption (A) or optical density (O.D.) A = log 10 (I o /I); % Transmission (%T) %T = I/I o; A = log 10 (1/ T);

34. II. Absorption Spectroscopy c. Setup parameters A or %T (y-axis) - A Wavelength range (x-axis) – 350 to 650 nm Wavelength increment – 5 nm Averaging time –0.1 s Spectral band pass – 2 nm

35. II. Absorption Spectroscopy d. Record Baseline (for specific setup parameters) Removes variations in: Throughput of reference and sample optics Detector sensitivity Run baseline for setup parameters and no sample inside spectrophotometer Store base line file Run a wavelength scan to make sure that absorbance (A) is zero at all wavelengths

36. Baseline Correction Wavelength (nm) Absorbance (O.D.) 0

37. II. Absorption Spectroscopy e. Sample and reference measurements Use identical cuvettes in sample and reference arms and ensure that they have the same path length; cuvette should have low absorption in region of interest Fill the sample cuvette with the sample of interest Fill the reference cuvette with everything in the sample cuvette, except the absorber Run a wavelength scan of the sample

38. Absorbance of Sample Wavelength (nm) Absorbance (O.D.) 0 4

39. II. Absorption Spectroscopy f. Considerations Dynamic range (limits on detector sensitivity) Typical dynamic range – 4 O.D. If sample has an absorbance of more than dynamic range of instrument – flat line Turbid Samples Light lost to scattering looks like absorption Need integrating sphere accessory to make accurate absorption measurements

40. Dynamic Range Wavelength (nm) Absorbance (O.D.) 4