Diffuse Optical Spectroscopy: Analysis of BiophotonicsSignals Short Course in Computational Biophotonics Albert Cerussi Day 4/Lecture #2

Transcription

1 Diffuse Optical Spectroscopy: Analysis of BiophotonicsSignals 2013 Short Course in Computational Biophotonics Albert Cerussi Day 4/Lecture #2

2 Disclosures No financial conflicts to disclose

3 Learning Objectives Control of optical pathlength (s) Wavelength (λ), Space(ρ,z), Time (t)/frequency (f) Controlling path length enables optical property measurement Absorption Coefficient (µ a ) Reduced Scattering Coefficient (µ s ) Quantify molecular absorbers Use of models to optimize information

4 Why do we care about modeling light transport in tissues? Some examples from this morning

5 Why Modeling Matters Phenylephrine Ephedrine Optical property change from pressor drug Absorption and/or scattering? Brain and/or skull/skin? L. Meng, et al. Brit J. Anes, 107, 209 (2011)

6 Why Modeling Matters ABSORPTION (mm -1 ) TISSUE SPECTRA LESION NORMAL WAVELENGTH (nm) Before Therapy FUNCTIONAL IMAGES Tissue Optical Index (TOI) = (HHb x H 2 O)/lipid Long term R(λ) changes related to tumor pathology How do we know changes are true tumor metabolism? LESION NORMAL ABSORPTION (mm -1 ) WAVELENGTH (nm) 3 Weeks Post Therapy Cerussi, A. E., et al. Phil Trans Roy Soc A, 369(1995), 2011

7 Why Modeling Matters Clinical outcome tied to optical measurement (threshold) Can better modeling improve this? M. Heringlakeet.al,, Anesthesiology V 114 (2011).

8 Why Modeling Matters ANCIENT SCRIPT MODERN SCRIPT BIOPHYSICAL STRUCTURE & FUNCTIUON OPTICAL MEASUREMENTS

9 What then is our goal?

10 What is Our Goal? Quantitative absorption/scattering NIR spectroscopy in turbid tissues purely absorbing with scatter I 0 I I 0 s = 10 mm S =? Beer-Lambert Law I log 0 I = ε cs ε = molar extinction c = absorber concentration s= photon path length (or L)

11 What is Our Goal Need to know & control photon path length (s) To get accurate molecular concentrations and states Cerussi A, et al J. Biomed Optics 10(5); 2005

12 The Key: Control Photon Pathlength Noted in the Previous lecture Control of pathlengthkey to diffuse optical imaging and spectroscopy WAVELENGTH TIME SPACE

13 Some Scales to Remember SCATTERING ABSORPTION SPACE l sc ~ 30 µm l abs ~100 mm TIME τ sc ~ 0.1 ps τ abs ~ 0.2 ns

14 Depths to Consider Diffuse Optical Spectroscopy for deep tissue Depths > 5mm Clinical Examples (non-invasive) Brain Breast Tumors Muscle

15 Models to consider Transport theory Analytic (eg diffusion) Numerical (NIRFAST, COMSOL) Monte Carlo (VP, MCML)

16 CW Intensity Characteristics

17 CW Light Distribution I 0 µ a = 0.01 mm -1 µ s = 1.0 mm -1 0 z [mm] ρ [mm] HOMOGENEOUS TISSUE

18 CW Light Distribution Diffusion Theory (INF) Φ,, ~ 1 3 Optical Diffusion Coefficient (mm) 3 Effective Attenuation Coefficient (mm -1 ) Optical Penetration Depth (mm)

19 CW Light Distribution I 0 R(ρ) LOG Φ µ a = 0.01 mm -1 µ s = 1.0 mm -1 0 z [mm] ρ [mm]

20 CW Light Distribution 0 REFLECTANCE I 0 ρ FLUENCE (au) RHO (mm) z [mm] ρ [mm]

21 CW Light Distribution 0 REFLECTANCE I 0 ρ FLUENCE (au) RHO (mm) z [mm] z ρ [mm] FLUENCE (au) DEPTH (mm)

22 Modeling Light Penetration Question: What wavelengths should we use for deep tissue penetration?

23 Modeling Light Penetration Consider homogeneous brain-like media: λ(nm) µ a (mm -1 ) µ s (mm -1 ) n

24 Modeling Light Penetration z [mm] Fluence of ρ and z ~ 450nm ρ [mm] LOG Φ

25 Modeling Light Penetration z [mm] Fluence of ρ and z ~ 450nm ρ [mm] 10 mw in LOG Φ atto-w 10-2 zepto-w 10 yocto-w

26 Modeling Light Penetration Fluence of ρ and z ~ 450nm LOG Φ 0 z [mm] ρ [mm]

27 Modeling Light Penetration Fluence of ρ and z ~ 750nm LOG Φ 0 z [mm] ρ [mm]

28 Modeling Light Penetration Fluence of ρ and z ~ 1200nm LOG Φ 0 z [mm] ρ [mm]

29 Modeling Broadband Light Penetration Question: How much will different NIR wavelengths penetrate tissues?

30 Modeling Broadband Light Penetration Optical Penetration Depth from Diffusion theory: = 4.35 ±0.68 mm

31 Modeling Broadband Light Penetration

32 Optical Property Recovery (CW) Question: How can we use this information to recover the optical properties of the tissue?

33 Optical Property Recovery (CW) MUS' (1/mm) MUA (1/mm) Φ,, ~ Diffusion Theory (INF) Diffusion Coefficient Effective Attenuation Coefficient

34 Optical Property Recovery (CW) MUS' (1/mm) = mm MUA (1/mm) Φ,, ~ Diffusion Theory (INF) Diffusion Coefficient Effective Attenuation Coefficient

35 Optical Property Recovery (CW) Spatially-Resolved Not always applicable NORM FLUENCE (au) / / /2.015 NORM FLUENCE (au) / / / RHO (mm) SCATTER DOMINATED RHO (mm)

36 Optical Property Recovery Question: Can we improve measurement sensitivity to the tissue optical properties? Want to separate absorption from scattering in thick tissues (>5mm)

37 Optical Property Measurement: Time Domain

38 Time Domain: How it Works PULSED LASER SCAN OVER λ AOTF BS FILTER TO FIBER PROBE SOURCE LASER PULSE (ps) TCSPC REF PD SCAN OVER T TISSUE RESPONSE (ns) DELAY LINE GATE PULSE APD FILTER Narrow FWHM Pulse (ps): Hi repetition rate (MHz) broadens (ns)

39 Time Domain: How it Works Real World: Detector responses broaden Convolutionof IRF and Tissue Response

40 Time Domain Light Propagation Diffusion Theory (Inf Med)

41 Time Domain (Diffusion Theory) ρ= 20 mm µ a = 0.01 mm -1 µ s = 1.0 mm -1

42 Time Domain (Diffusion Theory) SDA ρ= 20 mm µ a = 0.01 mm -1 µ s = 1.0 mm -1 NURBS

43 Time Domain (Diffusion Theory) SDA ADEQUATE DIFFUSION L 85 mm NURBS

44 Time Domain (Diffusion Theory)

45 Question: My data never looks like that

46 Time Domain Models: Monte Carlo ρ= 20 mm µ a = 0.01 mm -1 µ s = 1.0 mm -1

47 Time Domain Models: Monte Carlo ρ= 20 mm µ a = 0.01 mm -1 µ s = 1.0 mm -1 N σ

48 Question: How can we exploit temporal dependence to measure optical properties?

49 Optical Property Measurement (TD) Source 25 mm Detector Sample and discriminate short/long paths Laser pulse t 1 = 200 ps t 2 = 600 ps t 4 = 1400 ps Detected pulse Intensity t = 200 ps t = 200 ps t = 200 ps

50 Optical Property Measurement (TD) ρ= 20 mm

51 Optical Property Measurement (TD) ρ= 20 mm

52 Optical Property Measurement (TD) ρ= 20 mm

53 Shortcut: Theory of Moments I hate fitting Theory of moments Analytical Easy to include IRF Liebert et al., Appl Opt 42(28) 2003.

54 Question: How can we exploit temporal dependence to control penetration depth?

55 Time Domain: Time Gating

56 Time Domain: Time Gating LAYERED PHANTOM MEASUREMENT (830 nm) ρ= 5 mm MAINLY TOP LAYER 12 mm 100 mm mm mm mm mm -1 MAINLY BOTTOM LAYER

57 Optical Property Measurement: Frequency Domain

58 Frequency-Domain Measurements SOURCE φ TISSUE stuff happens DETECTED AMPLITUDE AC src AC det DC src DC det φ ~ time Μ ~ AC/DC TIME

59 Frequency-Domain Measurements Frequency Sweeps (50 to 500 MHz)

60 Calibration of IRF: No Convolution 7 x AMPLITUDE (au) x x PHASE (Deg) FREQUENCY (MHz) FREQUENCY (MHz)

61 Frequency-Domain Measurements TIME FREQUENCY FFT AMP PHASE Time & Frequency Domain are Fourier equivalents Experimental considerations dictate choice

62 Frequency Domain Light Propagation (SI) S( ω) 4πvD 2 2 A si ( ρ, ω) = ξ + η Θ η ρ, ω) = k imag ( ω) r arctan + φ ( ξ si ( 0 0 ω) Photon density amplitude Photon density phase where 1 ξ = exp r o [ k ( ω) r ] cos[ k ( ω)( r r )] exp[ k ( ω r ] real 0 imag 0b 0 real ) r0 b 1 0b η = sin 1 [ ( ω)( r r )] exp[ k ( ω r ] kimag 0 b 0 real ) 0b r0 b Cerussi, A. and Tromberg, B., "Photon migration spectroscopy: Frequency domain techniques," in Biomedical photonics handbook, Vo-Dinh, T., Ed., 1st ed.: CRC Press, 2003, pp

63 Frequency Domain: Diffusion Theory ρ= 20 mm µ a = 0.01 mm -1 µ s = 1.0 mm -1

64 Question: My data never looks like that

65 Frequency Domain Models: Monte Carlo

66 Optical Property Recovery Question: Can we improve measurement sensitivity to the tissue optical properties? Want to separate absorption from scattering in thick tissues (>5mm)

67 Frequency Domain:Evolution in f

68 Frequency Domain: Evolution in Rho PHASE (deg) FDPM MULTI-R PLOTS: LAMBDA = 850nm FREQ =204MHz PHASE (deg.) MHz 200 MHz DISTANCE (mm) DISTANCE (mm) LN(A) (au) LN(A) (a.u.) MHz 200 MHz DISTANCE (mm) DISTANCE (mm)

69 Frequency Domain: Evolution in Rho 0 FLUENCE (RHO = 0) 0 FLUENCE (RHO = 0) FLUENCE (au) FLUENCE (au) Z (mm) Z (mm)

70 Question: How can we exploit frequency dependence to measure optical properties?

71 Optical Property Measurement: Frequency Domain

72 Frequency Domain: Optical Properties ρ= 20 mm 0

73 Frequency Domain: Optical Properties ρ= 20 mm 0

74 Frequency Domain: Optical Properties ρ= 20 mm 0

75 Frequency Domain: Multi R, Single S 3430 FDPM MULTI-R PLOTS: LAMBDA = 850nm FREQ =204MHz PHASE (deg) DISTANCE (mm) 2 2 LN(A) (au) DISTANCE (mm) S. Fantini et al., Optical Engineering 34 (1996)

76 Optical Property Measurement: Imaging and Spectroscopy

77 Cant We all Just Get Along CW Spectroscopy: Many wavelengths Hard to quantify at depth with single ρ FD/TD Spectroscopy Easy to quantify at depth with single ρ Tougher for many wavelengths

78 Harmony of λand f MHz modulation INTENSITY ~.5 ms 401 frequency sweep TIME (µs) (ns) MHz (~ 200 ms)

79 Harmony of λand f 4.5 modulation diffusion model AMPLITUDE (a.u.) FREQUENCY (MHz) PHASE (deg) FREQUENCY (MHz)

80 Harmony of λand f 4.5 modulation diffusion model AMPLITUDE (a.u.) FREQUENCY (MHz) global fit PHASE (deg) FREQUENCY (MHz)

81 Harmony of λand f 4.5 modulation diffusion model AMPLITUDE (a.u.) FREQUENCY (MHz) global fit PHASE (deg) 40 optical properties FREQUENCY (MHz) 20

82 Harmony of λand f modulation diffusion model absorption & scattering ABSORPTION (mm -1 ) SCATTERING (mm -1 ) WAVELENGTH (nm) WAVELENGTH (nm)

83 Harmony of λand f modulation diffusion model absorption & scattering power law ABSORPTION (mm -1 ) SCATTERING (mm -1 ) WAVELENGTH (nm) scattering = SA λ WAVELENGTH (nm) SP

84 Harmony of λand f modulation diffusion model absorption & scattering broadband reflectance ABSORPTION (mm -1 ) REFLECTANCE (a.u.) WAVELENGTH (nm) WAVELENGTH (nm)

85 Harmony of λand f modulation diffusion model absorption & scattering broadband reflectance ABSORPTION (mm -1 ) REFLECTANCE (a.u.) WAVELENGTH (nm) scale w FDPM WAVELENGTH (nm)

86 Harmony of λand f modulation diffusion model absorption & scattering broadband reflectance ABSORPTION (mm -1 ) REFLECTANCE (a.u.) WAVELENGTH (nm) scale w FDPM WAVELENGTH (nm)

87 Harmony of λand f modulation diffusion model absorption & scattering broadband reflectance ABSORPTION (mm -1 ) FDPM BROADBAND FOUR COMPONENT FIT WAVELENGTH (nm)

88 Harmony of λand f modulation diffusion model absorption & scattering broadband reflectance chromophore fit ABSORPTION (mm -1 ) FDPM BROADBAND FOUR COMPONENT FIT WAVELENGTH (nm)

89 Harmony of λand f and ρ ABSORPTION (mm -1 ) mm 16mm 20mm 24mm 28mm 32mm WAVELENGTH (nm) ADIPOSE S D D GLANDULAR Two-layer phantom spectrum at different Source-Detector separations

90 Harmony of λand f and ρ BOTTOM LAYER TOP LAYER (6mm) A. Li et al, Applied Optics 46(21) 2007

91 Harmony of λand f and ρ 3D TUMOR PHANTOM (SINGLE λ) RECONSTRUCTION WITH NIRFAST 2cm 11mm depth H. Haghany, PHD Thesis, UCI 2013

92 Learning Objectives Control of optical pathlength (s) Wavelength (λ), Space(ρ,z), Time (t)/frequency (f) Controlling path length enables optical property measurement Absorption Coefficient (µ a ) Reduced Scattering Coefficient (µ s ) Quantify molecular absorbers Use of models to optimize information

93 Acknowledgements NCRR P41 Laser Microbeam and Medical Program NCI U54 Network for Translational Research NCI Chao Family Comprehensive Cancer Center Arnold and Mabel Beckman Foundation NCI R01CA American College of Radiology Imaging Networks (ACRIN) AFOSR Military Photomedicine Program UNIVERSITY of CALIFORNIA IRVINE