Advanced Microscopy. Wintersemester 2012/13 Alexander Heisterkamp Tissue Optics, Optical Clearing, Optical Tomography

Transcription

1 Advanced Microscopy Wintersemester 2012/13 Alexander Heisterkamp Tissue Optics, Optical Clearing, Optical Tomography

2 [Welch]

3 Radiometric variables Goal: calculation of the distribution of the optical field within the tissue air / water tissue

4 Tissue optics Assumptions and simplifications necessary: no wave properties (coherence, interference, polarisation, diffraction) => light is viewed as particle flow (valid for tissue thicknesses >> λ) no inelastic scattering (fluorescence, phosphorescence, raman scattering)

5 Radiometric variables commonly used values in optics: intensity (power density/irradiance) energy density (fluence) = Ιdt (radiant exposure =! J $ ) " # m 2 % & & W $ % cm Ι 2 #! " F & J # $ 2 % cm! " Power P (radiant power) = radiation flux Φ (flux) P = dq Φ = [ W ] dt Q : radiation energy

6 new: Radiometric variables & J # energy density (radiant energy density) W $ 3! % m " beam density (radiance) & W # L $ 2! % m sr " L describes the spatial distribution of the radiance: L( r, s, t) = dφ s da dω da dω$ da = n da

7 Absorption 1 absorption [µm -1 ] hemo- globine proteins melanin water nm 1µm wavelength 10µm

8 Diagnostic window of tissue µ µ Scattering

9 Absorp'on)and)sca-ering) Absorp'on) Within the UV and visible spectrum absorption is mostly dominated by: proteins, hemoglobine, melanin, etc. by excitation of electronic transitions. In the mid and far infrared (IR) the absorption of water within the tissue is dominating. Mainly oscillation bands are excited (O-H, N-H, C-H).

10 Absorp'on) Absoption coefficient: µ = a c a σa c a : absorber concentration [cm -3 ] σ a : abs.cross section [cm 2 ] Lambert-Beer: Ι T = Ι 0 e µ a z

11 Sca-ering) Scattering is always connected with a change in propagation direction. inelastic scattering: ( energy loss, i.e. change in wavelength)! fluorescence, phosphorescence! Brillouin scattering! Raman scattering elastic scattering: (no energy loss)! Rayleigh scattering! Mie scattering

12 Sca-ering&Absorp'on))) The scattering coefficient is defined in analogy to the absorption coefficient di a (z) dz = -µ s a I(z) di s (z) dz = -µ s I(z) µ a : absorption coeff. µ s : scattering coeff. attenuation is described by Beers law: I ( z ) = I ( R ) e 0 1 ( µ + µ ) a s z Extinction/attenuation coeff.: t a s

13 Sca-ering&Absorp'on) Albedo (also: scattering capability) a = µ s µ + µ a s = µ s µ t (a = 0, pure absorption; a = 1, pure scattering) Laser in der Medizin M. Frenz

14 Mean)free)path)length) The mean free path length is the depth, in which the intensity of the radiation was attenuated to 1/e (T = 37%). δ a = 1 µ a optical penetration depth (mean free path length) (37% are getting deeper than this!) probability to find number of photons in the depth of 2 δ a is roughly 13% 3 δ a " 5% 4 δ a " 2%

15 Sca-ering) problem: µ s is a direction-dependent variable and thus for aligned structures ( such as muscle fibers, dentin, photoreceptors etc.) a unsufficient description s s θ

16 Sca-ering)phase)func'on) probability of a single photon event, in which a photon from direction s is scattered into direction s. examples for scattering phase functions: Rayleigh scattering (isotropic: p ( ) c o n s t ) Mie scattering (forward scattering)

17 Sca-ering)phase)func'on) Rayleigh scattering: I 1 4 λ isotropic particle size << λ macromolecular structures (<10 nm) membranes (~100 nm) Mie scattering: I 1 λ forward particle size λ organelles ( > 100 nm) collagen fibers ( nm) cells ( > 5 µm)

18 Sca-ering)phase)func'on) )) µ) s)))[)c)m) B)1) ]) sca-ering)coefficient) 1000) 100) 10) 1) Mie)theory) Rayleigh)theory) Albino)rat)skin) 0) 1) 2) 3) 4) 5) wavelength)(µm))

19 approximation for biological tissue: Sca-ering)phase)func'on) 1. for non aligned tissues P depends only on the polar angle Θ and is independent of the azimutal angle ϕ. 2. the polar dependence is described by the Henyey-Greenstein-Funktion* : P HG ( s, s ) = P HG (cosθ) = 1 4π (1 + g 1 g 2 2 cos Θ) 3 2 * Henyey L, Greenstein J (1941): Diffuse radiation in the galaxy. Astrophys. J. 93, 70-83

20 Sca-ering)phase)func'on) g=0.9 g=0.8 g= Henyey-Greenstein-phase function for different g-factors

21 Sca-ering)phase)func'on) g = expected value of the cosine of the scattering angle (ratio between forward and backward scattering) g= <cos(θ)>= p(cosθ) cosθ dω 4π (cos Θ) dω = 1 4π p (normalized to 1)

22 Sca-ering)phase)func'on) 0 < g 1 : forward scattering is dominating g = 0 : isotropic scattering (p(cosθ)=1/4π) 1 g < 0 : backward scattering is dominating g(tissue) = equals scattering angle of Θ = 45 o - 8 o 1 after approx. - scattering events the photon looses 1 g it s memory of its former direction => random walk

23 Sca-ering)phase)func'on) for example yellow light in skin: λ = 577 nm, g = 0,8 (cos 37 = 0,8) 1 1 0, 8 the photon takes approx. = until it performs random-walk. 5 scattering events

24 Sca-ering)coefficient) ' = µ s (1- g) µ s forward scattering" reduced scattering coefficient µ s ' = µ t (1- g) + µ s µ a reduced total attenuation coefficient µ eff = 3 µ a ( µ s (1- g) + µ a ) effective attenuation coefficient (describes far field behaviour)

25 radia've)transport)equa'on) aim: description of radiance L( r, s, t) at r in the direction of s at the time point t! origin: 60-ties Chandrasekar describes light propagation in planetary and stellar atmospheres

26 radia've)transport)equa'on) 1 c L( r, s,t) t = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t)

27 1 c L( r, s,t) t radia've)transport)equa'on) = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t) change in radiance in direction s in the volume V 1 L( r, s, t) c V t dv

28 1 c L( r, s,t) t radia've)transport)equa'on) = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t) losses of the radiance at surface S of the volume V: S L( r, s, t) s ds = = V V ( L( r, s, t) s) dv s L( r, s, t) dv

29 1 c L( r, s,t) t radia've)transport)equa'on) = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t) absorption of radiance in the volume V µ a L( r, s, t) V dv

30 1 c L( r, s,t) t radia've)transport)equa'on) = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t) losses due to scattering in the volumen V µ sl( r, s, t) V dv

31 1 c L( r, s,t) t radia've)transport)equa'on) = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t) gain of radiance in the volume V from direction s in direction of s µ s P( s, s ) L( r, s, t) dω V 4π dv

32 1 c L( r, s,t) t radia've)transport)equa'on) = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t) gain of radiance due to sources in the volume V (for example fluorescence) ε( r, s, t) V dv

33 1 c L( r, s,t) t radia've)transport)equa'on) = S L( r, s,t) µ a L( r, s,t) µ s L( r, s,t) 4π + µ s P( s, s ) L( r, s,t)dω+ε( r, s,t) solution of the equation: complete analytical solution not possible best approximation depends on tissue geometry look for simplifications

34 radia've)transport)equa'on) 1st approximation: stationary equation S L( r, s,t) = µ t L( r, s,t)+ µ s analytical solution in some cases possible most simple case: 1dim. half-space, no scattering, no fluorescence 4π P( s, s ) L( r, s,t)dω+ε( r, s,t) dl(z) dz = -µ a L(z) Lambert-Beers law

35 sta'onary)radia've)transport)equa'on) 2nd simplification: discretization of the coordinates: dividing the solid angle in discrete directions (for example 2 or 7). oldest method: Kubelka-Munk-theory requirement: radiation is diffusely irradiated at the tissue and scattered diffusely

36 KubelkaBMunkBtheory) assumption: 1-dim geometry, µ a << µ s x = 0 dx x = d I I d J 0 J µ ~ a reflection: J R = I ~ µ s I T = d I transmission: due to scattering, two currents of light are propagating within the tissue, I, J. energy conservation: di dx dj dx = ~ µ I ~ µ I + ~ µ J s = ~ µ s J ~ µ a J + ~ µ si a s experimentally accesible variables: I, R, T

37 7)flux)model) similar as Kubelka Munk but 7 directions of flux incoming light six directions in space + irradiation direction advantage : implementation of a non isotropic scattering function y F - F - x F - z coll F + z F + x x F + F + y y

38 Diffusion)theory) 3rd simplification: r, s ( s, s ) radiance L( ) and phase function p are approximated by Legendre polynoms P l approx. up to l = 1 so called P1-approximation leads to diffusion theory but: difficult!

39 Diffusion)theory) simple derivation diffusion is dominating, if: mean free path length 1 µ t << dimensions of tissue a photon is scattered frequently before it is absorbed or leaving the tissue photon density N ( r, s ) is nearly constant in all directions s

40 diffusion equation: ), ( ), ( ) ( ), ( ), ( t r S t r E r µ t r E D t t r E c a + = ) ( ) ( ) ( r S r S r S + = ( ) ( ) g µ µ µ D s a tr + = = source diffusion constant Ficks law + energy conservation Diffusion)theory)

41 Diffusion)theory) attenuation of light inside tissue solution of the diff. equation 1 W 800 nm A 2 = 1 cm 3 ' 4π r µ det s e µ eff E = I r η = 1 0 fluence Ε [W/cm 2 ] r µ a =0.2, µ -1 s '=20 cm -50% +50% r [cm] photons / s

42 Diffusion)theory) normalized fluence as a function of optical depth in a semi-finite body with different albedos and isotropic scattering (g = 0) in tissue (refr. index n = 1 ) [Müller]

43 MonteBCarloBSimula'on) start 1 photon yes move photon Δ s internally reflected? no photon in tissue? change direction of photon no yes update reflection and transmission photon scattered? no photon absorbed? yes no no yes update absorption last photon? yes end

44 MonteBCarloBSimula'on)

45 MonteBCarloBSimula'on)

46 MonteBCarloBSimula'on) laser µ a = 1 cm -1 µ s = 100 cm -1 g = 0.9 N = photons n air = 1 n water = 1.33 H 2 O fluence 2 (W/cm ) refractive index n not matched (air) n tissue incoming power 1 refractive index n matched (water) depth (mm)

47 Scales and resolution in imaging 10)cm)) ) MRI) ultrasound) 1)cm)) 10000) FMT) sample)size) 1)mm)) 1000) 100)µm)) 100) mul'photon) OPT) OCT) optoacous'cs) 10)µm)) 10) 1)µm)) superresolu'on) (4Pi,)STED,)STORM,)PALM)) confocal) 1) 1) 2) 3) 4) 5) 1)µm)) 10)µm)) 100)µm)) 1)mm) resolu'on)

48 Tomography gr.:&τομος =&cut) gr.:)γραφή&=&wri+ng &&) Combination of volumetric imaging methods with sectioning imaging methods fundamentals of tomography were developed by Alessandro Vallebona 1930 in Genua (radiology) )Large scale imaging (mm sized samples) Optical Projection Tomography (OPT)

49 Sharpe et al. Tomography

50 Optical tomography 'me)window)to)discriminate)sca-ered)photons) snake) diffuse) ""ps) Time) 1"ns) ballis+c) Time) incident)) laser)pulse) inves'gated) 'ssue) detected) laser)light)

51 Optical tomography mamography)

52 Optical tomography mamography)

53 Sharpe et al. Tomography

54

55

56 Optical projection tomography The Electronic Atlas of the Developing Human Brain BMC)Neurosci.)2004;)5:) 27.)) Published)online)2004) August)6.)doi:) /1471B2202B5B27.) Approx.)day)41,)size) around)14mm)in)length) OPT"models"of"CS12"to"CS23."S'll)shots)of)the)le`)lateral)side)of)3)dimensional)OPT)models)of)human)embryos)spanning)the)major) period)of)organogenesis)(cs12bcs17).)the)developmental)stage)(e.g.)cs12),)specimen)number)(e.g.)n285))and)karyotype)for)each) model)are)given)underneath.)

57 Optical projection tomography

58 Optical projection tomography

59 P θ (t) is the Radon-transformation of the function f(x,y)! Line AB t = xcosθ + y sinθ P ( t) = θ ( θ, t) line f ( x, y) ds mit P ( t) = f ( x, y) δ ( x cosθ + y sinθ t) dxdy θ & 0 x 0 δ ( x) = % und δ ( x) dx = 1 $ x = 0

60

61 Sharpe et al. Tomography

62 Optical Projection Tomography 1 Laser 2 Shutter 3 Beam expander 4 Cuvette 5 Capillary 6 Specimen 7 Rotation mount 8 Microscope objective 9 Filter wheel 10 Iris aperture 11 Lens tube 12 CCD J.) Sharpe) et) al.,) Op'cal) Projec'on) Tomography) as) a) Tool) for) 3D) Microscopy) and) Gene) Expression) Studies,) Science) 2002)

63 Scanning Laser Optical Tomography Incuba'on) chamber) Rota'on) stage) Excita'on) Filter)Wheel) Contrast"mechanisms:" )Intrinsic)(Absorp'on/Sca-ering)) )Absorp'on) )Fluorescence)(1P)&)2P)) )HHG) 405nm" 445nm" x=y" Scanner" PD" Fluorescence) Filter)Wheel) Benefits:" )reduced)photo)bleaching) )285)'mes)higher)coll.)efficiency) )MP)compa'ble) )high)penetra'on)depth) 473nm" PMT" 532nm" 589nm" 635nm"

64 and other biological samples 300µm" Locusta(migratoria(brain" Caviidae)cochlea" BioarKficial"tooth" 300µm" 1mm" NP(labelled(( Zebrafish"

65 Optical projection tomography

66 Object:" Bacteria)on)dental)implant) Contrast"mechanism:" sca-ering/absorp'on) Biofilm imaging Contrast"marker:" Triphenyltetrazolium)Chloride)(TTC))")Triphenylformazan)(TPF))

67 Optical clearing Vascular)visualiza'on)of)whole)mount)embryo)a`er)an)in)vivo)intracardiac)microinjec'on)of)india)ink.)(A)) Control) embryo) at) day) 13.5;) vasculature) is) poorly) seen) without) ink.) (B)) Day) 13.5) embryo) a`er) le`) ventricular)microinjec'on)of)india)ink)in)utero)under)ultrasound)guidance.)the)ink)has)been)distributed) throughout) the) embryonic) vascular) system.) Embryo) 'ssues) were) cleared) with) a) benzyl) alcohol:benzyl) benzoate)mixture.)h,)heart;)li,)liver.)

68 Optical clearing

69 Tuchin et al

70 Tuchin et al

71 Tuchin et al

72 Optical clearing scale view

73 BABB cleared embryo Same embryo after fixation and staining Sharpe et al.

74 Optical tomography MSOT)Imaging) )reconstruc'on)of)light)distribu'on)in)'ssue)) (detec'on)by)ultrasound) )later)in)optoacous'cs))

75 Razansky et al. 2009, Nature Photonics

76 Razansky et al. 2009, Nature Photonics

77 Razansky et al. 2009, Nature Photonics