Theory of Frequency Sample Clauses

Theory of Frequency domain (FD) NIRS 19
Sample 1
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Theory of Frequency domain (FD) NIRS Photon diffusion equation. Photon transportation in biological tissues can be approximately treated as a diffusing process because scattering events dominate photon propagation inside the tissue [78, 79]. μs’ is often much larger (>10 folds) than μa in biological tissues. If one tracks the trajectory of each photon inside the tissue using Monte Carlo simulation, a random walking pattern would be observed. Photon propagation inside tissue as a diffusive process can be described by the photon diffusion equation [78, 88]. Specifically, the measured photon fluence rate Φ(r,t) (photons/[s∙cm2]) obeys the time-dependent photon diffusion equation in a homogeneous medium [78, 84, 88, 89]: (2.9) Here v (cm/s) is the speed of light in medium and D = v/3(μa + μs’) (cm2/s) is the photon diffusion coefficient. S(r, t) (photons/[s∙cm3]) is an isotropic source term which gives the number of photons emitted at position r and time t per unit volume per unit time. The right hand side (RHS) of Equation 2.9 shows the changing rate of photons within a sample volume. This rate equals the number of photons scattered into the volume per unit time from its surroundings (the first term on the left hand side (LHS) of Equation 2.9), minus the number of photons absorbed per unit time within the volume (the second term on the LHS), plus the number of photons emitted per unit time from any sources in the volume (the third term on the LHS) [84]. In case of FD NIRS, a frequency modulated source is used. Then the source term S(r,t) and photon fluence rate are written as ( ) (2.10)
Sample 1

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