ECEU 692 Subsurface Imaging Course Notes Part 2

ECEU 692 Subsurface Imaging Course Notes Part 2: Imaging with Light (3): Strong Scattering Profs. Brooks and Di. Marzio Northeastern University Spring 2004 February 2004 Chuck Di. Marzio, Northeastern University 1

Topic Outline • Our Old Scattering Model – What We Left Out • Phase Functions • Multiple Scattering • Computational Approaches – – Reduced Albedo Photon Migration Monte-Carlo A Simple 2 -Layer Model February 2004 Chuck Di. Marzio, Northeastern University 2

Recall Weak Scattering: What is Wrong? February 2004 Chuck Di. Marzio, Northeastern University 3

Imaging and Multiple Scattering Multi-View Tomography; (e. g. Diffusive Optical Tomography) Localized Probing; (e. g. Confocal microscopy, Optical Coherence Tomography, Two-photon microscopy) February 2004 Chuck Di. Marzio, Northeastern University 4

Single Scattering Phase Function 10057 p 2 -1 here February 2004 Chuck Di. Marzio, Northeastern University 5

Multiple Scattering (1) • Scattering Angles Add • Think in 2 Dimensions • Total is Sqi • PDF is Convolution of Individual PDF’s February 2004 Chuck Di. Marzio, Northeastern University 6

Multiple Scattering (2) • Computational Approaches – Reduced Albedo – Photon Migration – Monte-Carlo Put 10057 p 2 -2 here • Issues – Multiple Scattering – Internal Reflection • Integrated Fresnel February 2004 Chuck Di. Marzio, Northeastern University 7

Photon Migration • Assumptions • Solution – Radiative Transport Equation – Taylor Series for Radiance – Boundary Conditions • Result – Photon Density Wave • DC or AC – Complex k (Lossy Wave) – Details Another Day – Diffusion-Like Equation for Photon Density February 2004 Chuck Di. Marzio, Northeastern University 8

W’, Transport Albedo Reflection vs. Albedo: Example Patterson, Michael S. , Ephraim Schwartz, and Brian C. Wilson, “Quantitative Reflectance Spectrophotometry for the Noninvasive Measurment of Photosensitizer Concentration in Tissue During Photodynamic Therapy, ” Photodynamic Therapy Mechanisms, SPIE Volume 1065, 1989. Pp. 115 --122. February 2004 Chuck Di. Marzio, Northeastern University 9

Monte-Carlo Models • Loop on Photons – Launch – Loop on Particle • Random Distance • Scatter or Absorb • Random Angle • Widely Applicable • Accurate Phase Function not Needed? • Computationally Intensive – Exit - Save Data • Compute Statistics February 2004 Chuck Di. Marzio, Northeastern University 10

Monte-Carlo Operation 1 c. Scatter or Absorb 1 a. Launch 1 b. Random Distance 1 d. Random Direction 1 e. Continue or Exit: If Exit, count as Reflection or Transmission February 2004 2 -N. Next Photons N+1. Summarize Refl Statistics Radius Chuck Di. Marzio, Northeastern University 11

Simple Skin Model Rsc • Rsc and Re Re – No desired signal • Rd < Rd (no blood), Rd(l) Stratum Corneum – Rd contains wanted signal 100 mm Epidermis • Neglecting – index of refraction changes – multiple scattering between layers Arterial Hb 2 mm Venous Hb Dermis – specular reflections. Thanks to Peter Dwyer at Lucid Technologies and MGH February 2004 Chuck Di. Marzio, Northeastern University 12

Optical Properties of Human Tissue Hb. O 2 Melanin Epidermis Absorption Hb Dermis Scattering Epidermi s Dermis, Hb. O 2 Anisotropy Hb, Hb. O 2 Dermis Water February 2004 Chuck Di. Marzio, Northeastern University Epidermis 13

Sample Monte-Carlo-Model Spectra for Tissue Inputs: • Epidermis = 0. 065 mm • Dermal Hb = 0. 12 m. M No Hb Hb. O 2 Outputs: • Reflectance (Shown) • Radially Resolved Reflectance • Angular Resolved Reflectance February 2004 Chuck Di. Marzio, Northeastern University Hb 14

Simplified Skin Model Equations R = Rsc + Re + Rd + February 2004 Chuck Di. Marzio, Northeastern University Hb Spectral Signatures 15

Simplified Skin Model Equations (Cont. ) • Want to find s = oxygen saturation of Hb • ma depends on s ma = koxycs + kdeoxyc(1 -s) + ma 0 koxy = Molar absorption coefficient of oxy-Hb kdeoxy = Molar absorption coefficient of deoxy-Hb c = Concentration of Hb s = Oxygen saturation fraction ma 0 = Other chromophores besides blood • Approximation: wavelengths close together only ma depends on l February 2004 Chuck Di. Marzio, Northeastern University 16

Simplified Skin Model Equations (Cont. ) • Grouping some variables together, to solve for s • Four equations, four unknowns February 2004 (BC) A R 0 s Chuck Di. Marzio, Northeastern University 17