6715_Lecture8 - Lecture VIII 1 2 3 4 5 6 VIII1 The...

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1 PHYS 6715 - Lecture VIII 1 Lecture VIII The Diffusion Model 1. The diffusion approximation 2. A boundary-value problem 3. The Green function method 4. Similarity principle 5. Boundary condition 6. Solving the BVP PHYS 6715 - Lecture VIII 2 Different components of light The light radiance L in a turbid medium can be separated into two major components: one with unscattered light Æ the primary component L p one with scattered light Æ L s The distribution of the primary component L p is correlated with the incident light on the turbid medium but reduces exponentially as exp{- μ t d} with d as the pathlength Æ for μ t =10(mm -1 ), only about 10% photons from an incident light beam or internal light source belong to the primary component after traveling over a distance of d c =0.23mm VIII–1 Diffusion Approximation PHYS 6715 - Lecture VIII 3 Different components of light The scattered component has a much more complicated distribution so we further divide it into two sub-components: those being scattering only a few times Æ “snake” sub-component those being scattered many times Æ diffuse sub-component The snake sub-component still has a strong correlation with the incident light and can be detected using the coherence technique Æ Optical coherence tomography (OCT) The diffuse sub-component essentially lost its correlation with the incident light and can be well described by a diffusion approximation to the radiative transfer equation Æ Diffuse Optical Tomography (DOT) VIII–1 Diffusion Approximation PHYS 6715 - Lecture VIII 4 VIII–1 Diffusion Approximation Different components of light Diffusion approximation of radiative transfer equation – neglect the portion of light scattered only a few time or less. Diffuse component Snake component absorbed component incident light tissue primary component 5 VIII–1 Diffusion Approximation Separation of RTE Let L( r , s )=L p ( r , s ) + L s ( r , s ) and denote as 4 ( , ) ( ) ( , ) ( , ') ( , ') ' ( , ) s a s e L L p L d s π μ μ μ ε = − + + Ω + r s r s s s r s r s ( , ) ( , ) p t p L L s μ = − r s r s 4 ( , ) ( , ) ( , ') ( , ') ' ( , ) ( , ) s t s s s p e L L p L d s π μ μ ε ε = − + Ω + + r s r s s s r s r s r s ( , ) L s r s ⋅∇ s A. Ishimaru, Wave propagation and scattering in random media , vol.1 (1978) 4 ( , ) ( , ') ( , ') ' p s p p L d π ε μ = Ω r s s s r s PHYS 6715 - Lecture VIII 6 VIII–1 Diffusion Approximation The scattered component The 2 nd equation containing both of the primary and scattered components is much harder to solve The way out is to replace the scattered component with its diffuse sub-component or ignore the snake sub-component L p ( r , s ) Φ s ( r )
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