February 2004 Chuck DiMarzio, Northeastern University a-1 ECEU692 Subsurface Imaging Course Notes Part 2: Imaging with Light (3): Strong Scattering Profs. Brooks and DiMarzio Northeastern University Spring 2004

February 2004 Chuck DiMarzio, Northeastern University a-2 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 DiMarzio, Northeastern University a-3 Recall Weak Scattering: What is Wrong?

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

February 2004 Chuck DiMarzio, Northeastern University a-5 Single Scattering Phase Function 10057p2-1 here

February 2004 Chuck DiMarzio, Northeastern University a-6 Multiple Scattering (1) Scattering Angles Add Think in 2 Dimensions Total is    i PDF is Convolution of Individual PDF’s

February 2004 Chuck DiMarzio, Northeastern University a-7 Multiple Scattering (2) Computational Approaches –Reduced Albedo –Photon Migration –Monte-Carlo Issues –Multiple Scattering –Internal Reflection Integrated Fresnel Put 10057p2-2 here

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

February 2004 Chuck DiMarzio, Northeastern University a-9 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, Pp

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

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

February 2004 Chuck DiMarzio, Northeastern University a-12 Simple Skin Model sc Epidermis Dermis R e R d ( ) Venous Hb Arterial Hb R 100  m 2 mm Stratum Corneum R sc and R e – No desired signal R d < R d (no blood), –R d contains wanted signal Neglecting –index of refraction changes –multiple scattering between layers – specular reflections. Thanks to Peter Dwyer at Lucid Technologies and MGH

February 2004 Chuck DiMarzio, Northeastern University a-13 Optical Properties of Human Tissue HbO 2 Hb Water Melanin Epidermis Dermis Absorption Dermis Epidermis Dermis, Hb, HbO 2 Scattering Anisotropy Hb, HbO 2

February 2004 Chuck DiMarzio, Northeastern University a-14 Sample Monte-Carlo-Model Spectra for Tissue Inputs: Epidermis = mm Dermal Hb = 0.12 mM Outputs: Reflectance (Shown) Radially Resolved Reflectance Angular Resolved Reflectance

February 2004 Chuck DiMarzio, Northeastern University a-15 R = R sc + R e + R d Simplified Skin Model Equations R = R sc + R e + R d Hb Spectral Signatures +

February 2004 Chuck DiMarzio, Northeastern University a-16 Simplified Skin Model Equations (Cont.) Want to find s = oxygen saturation of Hb  a depends on s  a =  oxy cs +  deoxy c(1-s) +  a0  oxy = Molar absorption coefficient of oxy-Hb  deoxy = Molar absorption coefficient of deoxy-Hb c = Concentration of Hb s = Oxygen saturation fraction  a0 = Other chromophores besides blood Approximation: wavelengths close together only  a depends on

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