Optical properties vs Optical measurements
Biomedical Optics
Tissue optical properties
E. Göran Salerud
• refractive index
n
• absorption
µa
• scattering
µs
• anisotropy
g
• reduced scattering
µs(1-g)
• transmission
T
• reflectance
R
Department Biomedical Engineering
Experiment: milk
Optical Properties of Tissue
• Absorption cross section
• Absorption coefficient
• Scattering cross section
• Scattering coefficient
• Phase function
• Scattering –anisotropy
• Reduced scattering coefficient
• (Reduced) albedo
The refractive index n
• Wave fronts from a point source in the context of
Snell's law. The region below the gray line has a
higher index of refraction and proportionally lower
wave velocity than the region above it.
The refractive index n
•
Refraction index
The dimensionless quantity n(w), index of refraction, is the ratio
of the speed of the light in vacuum to the speed of the wave in
the material.
 λ ) = n(λ ) − iα (λ )
n(
 λ )] = n(λ )
Re [ n(
n (ω ) = εr µr ≅ 1+ χ (ω ) if absorption negligible
ω
ω
n(ω ) =
1+ χ (ω )
c
c
" c %
''
v = $$
# n (ω ) &
N ≡ ( n+iκ ) if absorption plays a roll
cm ( λ ) =
k=
k=
λ
n(λ )
c c
f = = m
λ λm
λm =
(n+iκ )ω
c
4πκ ( λ )
µa (λ ) =
λ
Absorption, Fluorescence and Scattering
Absorption
Scattering
Light Transport
Model
Reflectance
c
n(λ )
Intrinsic
Fluorescence
Light Transport
Model
Absorption, Fluorescence and Scattering
Absorption
Fluorescence
Beer’s Law
Fluorescence
Concentrations
Scattering
Mie Theory
Scatterer size, density
Refractive index, etc
Jablonski diagram
Energy Levels
Energy levels are characteristic states of a molecule
• Translational - motion of the molecule’s center of mass
through space
• Spin - nuclear and electron spin
• Rotational - rotation of the molecule about its center of mass
• Vibrational - vibration of the molecule’s constituent atoms
• Electronic - interactions of the electrons and nuclei within a
molecule
Energy Levels
Energy
Energy Level Separation
(J)
Translation
Very small
Spin
10-32
Rotation
10-28
Vibration
10-25
Electronic
10-19
Energy Level example
• When a 514 nm photon from an argon ion laser is absorbed
by a hemoglobin molecule it will transfer its energy to the
hemoglobin molecule:
hc / λ = 6.62618⋅10 −34 ⋅ 3.0 ⋅108 / 514 ⋅10 −9 = 3.86 ⋅10 −19
• The photon is absorbed by the heme chromophore within the
hemoglobin protein. The heme choromophore is roughly 1
nm is size.
• After the heme chromophore absorbs one photon, the jump
in energy density is roughly the photon energy divided by a
nm3 volume:
−19
-7
3
3.86 ⋅10
/ 10 = 387 ⎡⎣ J / cm ⎤⎦
• The energy density of boiling water is 418 [J/cm3]
Electronic transitions
Mechanism of light absorption
What's quantized:
angular momentum = n × !
Consequently:
me 4 æç 1 1 ö÷
DE =
×
8e 0 h 2 çè ni2 n 2f ÷ø
energy
4
3
2
outer shell: n>1
13.7 eV = 91 nm
1
Biologically: typically UV or blue
Vibrational transitions
Rotational transitions
energy
What's quantized:
angular momentum L2 = J (J + 1)! 2
r
What's quantized:
Consequently:
oscillator levels : DEn®n+1 = !w
!
r - r0 » 0.5A
Representative values:
U » 5 eV
r0
r
U » 12 k (r - r0 ) ® k ~ 6 ´10 2 J/m 2
µ = 6 amu (2 carbon nuclei)
!2
DEJ ® J +1 = 2 × J
µr
2
® w = k µ = 2.5 ´1014 rad/sec
l = 6 µm
mid-IR
Representative values:
» 2 ´10 -3 eV
l0®1 » 0.5 mm
microwave regime
µ = 6 amu
!
r =1A
Absorption
Absorption
•
Extraction of energy from light by a molecular species
•
•
Diagnostic applications: Transitions between two energy levels
of a molecule that are well defined at specific wavelengths
could serve as spectral fingerprint of the molecule
•
Various types of Chromophores (light absorbers) in Tissue
•
Wavelength-dependent absorption
•
Tumor detection and other physiological assessments (e.g.
pulseoximetry)
Absorption occurs when the photon frequency matches the
“frequency” associated with the molecule’s energy transition
•
Electrons absorb the energy of the light and transform it into
vibrational motion
•
The absorption of a photon results in:
•
Therapeutic applications: Absorption of energy is the primary
mechanism that allows light form a source (laser) to produce
physical effects on tissue for treatment purpose
17
•
quantized change in charge separation
•
quantized excitation of vibrational modes
Electrons interact with neighboring atoms => convert vibrational
energy into thermal energy
18
Absorption
• Absorption is the annihilation of photonic
energy while interacting with
• electrons,
Absorption
In biomedical optics, absorption of photons is a most
important event:
•
• atoms, or
•
• molecules and the conversion into
•
heat or into
•
photons with a much lower frequency, e.g.,
•
flourescence or
•
phosphorense
Absorption is the primary event that allows a laser or other light
source to cause a potentially therapeutic (or damaging) effect
on a tissue.
•
Without absorption, there is no energy transfer to the tissue and the
tissue is left unaffected by the light.
Absorption of light provides a diagnostic role such as the
spectroscopy of a tissue.
•
Absorption can provide a clue as to the chemical composition of a
tissue, and serve as a mechanism of optical contrast during
imaging.
Chromophores
Vibrational transistion
• Molecules that absorb light are called chromophores
• There are two major types of absorption processes:
• vibrational transitions
• electronic transitions
Symmetrical stretching
n = 3652 cm-1
l = 2.738 µm
Vibrational transistion
Scissor stretching
n = 1595 cm-1
l = 5.128 µm
Asymmetrical stretching
n = 3756 cm-1
l = 2.662 µm
Absorption spectrum of water
Biological Chromophores
Absorption
Biological chromophores
Highly conjugated double bond systems
1. The peptide bonds and amino acids in proteins
•
Spectrum is often in the visible region
•
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
2. Purine and pyrimidine bases in nucleic acids and
their derivatives
3. Highly conjugated double bond systems
Biological Chromophores
Amino acids
Biological Chromophores
Bases and their derivatives
Molecule
l (nm)
e (x10-3) (cm2.mol-1)
Tryptophan
280, 219
5.6,47
Tyrosine
274,222,193
1.4,8,48
Phenylalanine
257,206,188
0.2,9.3,60
Histidine
211
5.9
Cystine
250
0.3
Molecule
l (nm)
e (x10-3) (cm2.mol-1)
Adenine
260.5
13.4
Adenosine
259.5
14.9
NADH
340,259
6.23, 14.4
NAD+
260
5.9, 18
Electronic transition
pyroles
porphyrins
heme
chlorophyl
cytochromes
phycobiliproteins
carotenoids
ferredoxins
flavins
melanin
Porphyrin
N
N
N
N
N
Lipids
Heam B
14,00
Absorption coefficient [m-1]
12,00
10,00
8,00
6,00
4,00
2,00
0,00
430
530
630
730
830
930
Wavelength l [nm]
1030
1130
Hemoglobin
Hemoglobin
at isosbestic point,
µ a = 0.023 mM × 0.09 mm-1 / mM = 0.002 mm-1
courtesy V. Venugopalan, http://www.osa.org/meetings/archives/2004/BIOMED/program/#educ
Mean free absorption pathlength = 500 mm (!)
Fluorescence Spectroscopy
A fluorescence scenario
Major biological fluorophores:
• structural proteins: collagen and
elastin crosslinks
• coenzymes for cellular energy
metabolism (electron acceptors):
• flavin adenine dinucleotide
(FAD)
• nicotinamide adenine
dinucleotide, reduced form
(NADH)
• aromatic amino acids: side groups
on proteins
• porphyrins: precursors to heme
Ref. Mycek and Pogue, Handbook of Biomedical Fluorescence
cellular epithelium
thickening
collagen support
healthy
•
increased FAD fluorescence
•
reduced collagen fluorescence (farther from surface)
•
courtesy M.-A. Mycek
trending towards cancer
polyp formation → neovasculature; increased
absorption & decreased fluorescence
How to talk about absorption
I0
Absorption - Beer-Lambert law
The decline of irradiance of the
amount dI0 of EM radiation is
proportional to the incident
quantity I0 and the distance dl
§
I
L
I
= 10 -e cL = e - µ a L
I0
I0 at l (I0(l)),
§
Amount of absorption (a),
§
Thickness layer (dl)
∂I = −I ⋅ α ⋅ ∂l
I1 = I 0 e − α l
µ a º ln10 × ec
molar extinction
§
"absorption coefficient" [1/length]
§
Dimension of a?
§
a = ec
concentration
Absorption Coefficient
Absorption
•
Beer’s law
Assumptions
•
• The transmitted intensity (I) is defined as:
I = I o 10 −ε cL
•
Where,
e is the molar extinction coefficient (1/mM.cm)
•
C is the concentration (mM)
L is the path length (cm)
Io is the initial intensity
40
Cross section is independent of relative orientation of the impinging
light and absorber uniform distribution of Na (molecules/cm3)
identical absorbing particles
Absorption Coefficient, µa [1/m]
•
µa=Nasa
•
Absorption cross-sectional area per unit volume of medium
Absorption mean free path, la [m]
#
•
!=
•
Represents the average distance a photon travels before being
absorbed
µa
Absorption Coefficient
Absorption Coefficient
Beer’s law in exponential form
The absorption coefficient
• The transmitted intensity (I) is defined as:
• The absorption coefficient (µa) is defined as:
I = I o e−2.303ε cL = I o e−µa L
µa = 2.303ε C
Where,
e is the molar extinction coefficient (1/mM.cm)
Where,
C is the concentration (mM)
e is the molar extinction coefficient (1/mM*cm)
L is the path length (cm)
C is the concentration (mM)
Io is the initial intensity
Absorption
Determining Concentrations (C)
Modes of measurement
Absorption (A) or optical density (O.D.)
A = log10 (Io/I);
% Transmission (%T)
Absorbing sample
of concentration C
I0
I
%T = I/Io; A = log10 (1/ T);
Path length, L
log10
Io
= ε ( λ ) CL
If
Absorption
Absorption
Sample and reference measurements
Chopper
BS
M
R
Detector
•
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
Electronics
S
Monochromator
White
Light
I
BS
Io
M
Sample
Chamber
Absorbance
Absorption
Optical density per unit length
A
1
1
1
I
ODλ = λ = log10 ( ) = − log10 ( )
x
x
T
x
I0
1
I
ODλ = Aλ = log10 ( ) = −log10 ( )
T
I0
ODλ = Aλ = log10 (e)µa x = εcx
ε = extinction coefficient
48
Absorption coefficient µa
abs. crosssectional area
Absorption coefficient
efficiency
σ a = Qa A
abs. crosssectional
area
geometrical area
µa = ρ aσ a
[cm 2 ] = [−][cm 2 ]
density
A
geometrical
cross-section
L is a photon's path length of travel.
The probability of survival (or
transmission T) of the photon after a
path length L is:
σ a = Qa A
T = exp[−µa L]
effective
cross-section
ECE532 Biomedical Optics
©Steven L. Jacques, Scott A.
Prahl
Oregon Graduate Institute
ECE532 Biomedical Optics
©Steven L. Jacques, Scott A.
Prahl
Oregon Graduate Institute
Absorption coefficient
T = exp[−µa L]
Related properties
abs. crosssectional area
µa = ρ aσ a
•
Attenuation coefficient is essentially (but not quite always)
synonymous with absorption coefficient
•
Molar absorption coefficient or Molar extinction coefficient, also
called molar absorptivity, is the absorption coefficient divided by
molarity (and usually multiplied by ln(10), i.e. decadic)
•
Mass attenuation coefficient, also called mass extinction
coefficient, is the absorption coefficient divided by density
•
Absorption cross section and scattering cross section are both
quantitatively related to the absorption coefficient (or
attenuation coefficient)
•
The absorption coefficient is also sometimes called opacity
density
The reciprocal of the absorption mean free path length
1
i
µa =
=
mfpa fp1 + fp2 ....... fpi
Bilirubin
Absorption
• The structure of bilirubin.
Wavelength dependence of absorption
• The diameter is approximately 1nm
•
In the ultraviolet and blue, the absorption increases with shorter
wavelengths due to protein, DNA and hemoglobin
•
In the red to near-infrared (NIR), hemoglobin is the primary
absorber in tissue and the absorption coefficient is much lower
than in the UV-VIS
• the geometrical area is A = 7.8x10-15 cm2.
Bilirubin spectrum
Example
•
At 460 nm, the extinction coefficient of bilirubin is e = 53846
•
If C is concentration [M] and L is path length [cm]. Therefore,
•
µa = eC ln(10)
•
A typical jaundiced neonate might have a bilirubin concentration of 10
mg/dl, or (0.100 g/liter)/(574.65 g/mole) = 0.17x10-3 M/L.
•
The bilirubin absorption coefficient at 460 nm is roughly
•
µa = eC ln(10) = (53846 [cm-1M-1])* (0.17x10-3 M)(2.303) = 21 cm-1.
•
If the concentration C is equivalent to
ra =(0.17x10-3 [moles/liter])* (6x1023
[mole-1])/ (1000 cm3/liter] = 1.02x1017
[cm-3]
•
The efficiency of absorption is
estimated: Qa = µa/(ra A) =
(21 [cm-1])/((1.02x1017 [cm-3])*
(A = 7.8x10-15[cm2])) = 0.026
•
The effective cross-section is
sa = Qa A = (0.026)(7.8x10-15 [cm2]) =
2.1x10-16 [cm2].
•
Bilirubin's effective cross-sectional
diameter is 0.16 nm or 16% the size of
its geometrical diameter.
[cm-1M-1]
Extinction coefficient
60000
50000
40000
30000
20000
10000
0
240
340
440
540
Wavelength (nm)
640
740
Absorption Spectrum of Human Tissue
Absorption
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
650 nm
Absorption is Caused by Multiple Chromophores
Typical tissue absorption!
adipose tissue ~ 1% blood by
volume
blood = 45% red blood
cells by volume
Hemoglobin molecular weight = 65,000 mg/mmole
Hb concentration = 23 mM
1.3µm
red blood cell = 1/3
hemoglobin by weight
single
absorber :
two
absorbers :
Hemodynamics calculations
µ a = ln10 × ec
ée
é µ a1 ù
ê µ ú = ln10 × êe
ê
ê a2 ú
ê !
êë ! úû
ë
Hb
1
Hb
2
measure the
absorption coefficients
parameters
of interest :
ù Hb
úé c ù
ú êc HbO2 ú
û
! úû ë
HbO2
1
HbO2
2
look up the molar extinction
coefficients (e.g.
http:/omlc.ogi.edu)
oxygen saturation:
total hemoglobin
e
e
Most comman Hb-spectra
[HbO2 ]
[Hb] + [HbO2 ]
[Hb]+ [HbO2 ]
calculate the
concentrations
• If the hemoglobin molecule
is bound to oxygen then
one has oxy-hemoglobin
or Hb02 [blue]
• If the hemoglobin molecule is bound to nothing then
one has deoxy-hemoglobin
or Hb [red]
theory works for N>2
chromophores, too!
ECE532 Biomedical Optics
©Steven L. Jacques, Scott A.
Prahl
Oregon Graduate Institute
Less common spectra of blood
• If the hemoglobin molecule is bound to carbon
monoxide then one has carboxy-hemoglobin or
HbCO
• If the hemoglobin molecule has broken down then
one has meta-hemoglobin.
Therapuetic or diagnostic window
• In the red to near-infrared (NIR), absorption is
miminal
• Absorption is the primary event that allows a laser or other
light source to cause a potentially therapeutic effect on a
tissue. Without absorption, there is no energy transfer to the
tissue and the tissue is left unaffected by the light.
• Absorption of light provides a diagnostic role such as the
spectroscopy of a tissue
Melanin
•
Melanin is a very complex absorbing material. Melanins from
natural sources fall into two general
•
eumelanin
•
•
A black-to-dark-brown insoluble material found in human black hair and
in the retina of the eye.
pheomelanin
•
•
Melanin Spectra
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”.
The melanins are considered to be polymers, however, the
details of the polymerization and the role of protein linkages in
the natural melanin complex are not known.
65
66
The absorption coefficient of the melanosome
interior
67
Absorption coefficient of melanosomes, μa
68
•
Measure the optical transmission through individual
melanosomes using a microscope and calculate μa from the
attentuated transmission.
•
Measure the threshold pulsed laser radiant exposure that
causes explosive vaporization of melanosomes and deduce μa
Optical depth of the epidermis, d
•
If one is interested in the amount of light transport into the skin
and out of the skin which is important for dosimetry of laser
treatments and interpretation of optical spectroscopy and
imaging, then one would like to know the optical depth (μad,
where d is epidermal thickness) of the epidermis. The epidermis
is so thin that its optical effect can be treated as a simple
absorption filter (epidermal transmission T = exp(-μad) for
collimated beam normal to skin surface).
69
•
The concentration of melanin within melanosomes is quite
variable. Ten-fold variation is to be expected.
•
However, the general shape of the melanosome absorption
spectrum is approximated:
•
•
μa = 1.70x1012 nm-3.48 [cm-1] for skin
•
μa = 6.49x1012 nm-3.48 [cm-1] for retina
where nm refers to the wavelength expressed in nanometers.
70
Concentration of Melanosomes
71
Concentration of Melanosomes
The skin
Skin Model 1
Skin Model 2
I ( λ) = I0 ( λ ) ⋅ Rd ( λ) ⋅ e−2ε m ( λ) c m lm −2ε h ( λ) c h lh
ITOT = I0 ( R1 + T12 ⋅ R2 + T12 ⋅ T22 ⋅ R3 + T12 ⋅ T22 ⋅ T32 ⋅ R4 )
€
€
Epidermis
•
Epidermis
The total optical absorption coefficient (µa.epi) of the epidermis
depends on a minor baseline skin absorption and a dominant
melanin absorption due to the melanosomes in the epidermis.
Bloodless rat skin
•
Baseline absorption coefficient of melaninless epidermis
Neonatal skin
•
Absorption coefficient of a single melanosome
•
Volume fraction of melanosomes in epidermis
•
Net epidermal absorption coefficient
Based on vaporization
Epidermis
Net epidermal absorption coefficient of
epidermis
Skin type
Fraction melanin
µa.epi = (f.mel)(µa.mel) + (1 - f.mel)( µa.skinbaseline)
light-skinned adults
f.mel = 1.3-6.3%
f.mel ≈ 10%
moderately pigmented adults
f.mel = 11-16%
wavelength [nm]
µa.skinbaseline [cm-1]
µa.mel [cm-1]
µa.epi [cm-1]
darkly pigmented adults
f.mel = 18-43%
694 nm
0.268
228
23
755 nm
0.254
172
17
1064 nm
0.244
55
5.7
µa.epi = (f.mel)( µa.mel) + (1 - f.mel)( µa.skinbaseline)
Absorpion coefficient of epidermis
Dermis
•
The total optical absorption coefficient (µa.derm) of the dermis
depends on a minor baseline skin absorption and a dominant
hemoglobin absorption due to the cutaneous blood perfusion.
•
Baseline absorption coefficient of bloodless dermis
•
•
Absorption coefficient of whole blood
•
ECE532 Biomedical Optics
©Steven L. Jacques, Scott A.
Prahl
Oregon Graduate Institute
µa.skinbaseline
µa.blood
Absorption coefficient of whole blood
Absorption coefficient of whole blood
at isosbestic point,
µ a = 0.023 mM × 0.09 mm-1 / mM = 0.002 mm-1
Mean free absorption pathlength = 500 mm (!)
courtesy V. Venugopalan, http://www.osa.org/meetings/archives/2004/BIOMED/program/#educ
Dermis
The total optical absorption coefficient (µa.derm) if the dermis is
perfused with blood
•
Absorption coefficient of dermis perfused with blood
• µa.derm=(fblood)(µa.blood) + (1-fblood)(µa.skinbaseline)
4
µs’
3
Attenuation coefficients
•
Absorption coefficients in skin
3
µa
2
2
1
1
0
600
650
700
750
800
850
Wavelength [nm]
900
950
1000
1050
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