title: On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium.
abstract: This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source–detector separations on a sphere of 50 mm radius with μa=0.01  mm(−1) and μ′s=1.0  mm(−1) are on average less than 5% different. The approximation for sphere, generally valid for a diameter≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source–detector separation.
authors.affiliation: Oklahoma State University, School of Electrical and Computer Engineering, Stillwater, Oklahoma 74078, United States.
authors.forename: Daqing
authors.initials: D
authors.lastname: Piao
authors.affiliation: SUNY Downstate Medical Center, Department of Pathology, Brooklyn, New York 11203, United StatescNIRx Medical Technologies LLC, Glen Head, New York 11545, United States.
authors.forename: Randall L
authors.initials: RL
authors.lastname: Barbour
authors.affiliation: NIRx Medical Technologies LLC, Glen Head, New York 11545, United States.
authors.forename: Harry L
authors.initials: HL
authors.lastname: Graber
authors.affiliation: University of Oklahoma College of Medicine, Department of Surgery, Oklahoma City, Oklahoma 73104, United States.
authors.forename: Daniel C
authors.initials: DC
authors.lastname: Lee
mesh_terms: D003198:Computer Simulation; D007259:Infrared Rays; D008954:Models, Biological; D009391:Nephelometry and Turbidimetry / Q000379:methods*; D012542:Scattering, Radiation; D019265:Spectroscopy, Near-Infrared / Q000379:methods*