Inhomogeneity Detection in Diffuse Optical Tomography Using Conformal Mapping Potlov A.Yu., Proskurin S.G., Frolov S.V. Biomedical engineering, TSTU Russia Saratov Fall Meeting 2013

Time Point Spread Function (TPSF) optical pulse diffusely transmitted through highly scattering tissue like phantom I – early arriving photons, II – mean time of flight, III – late arriving photons

Experimental setup

Comparison of simulated and experimentally acquired TPSF homogeneous case

Numerical simulation of TPSF homogeneous case inhomogeneous case good agreement with experiment is reached for late arriving photons

numerical simulation distribution of photon density in a cylindrical phantom at 0,7 ns. homogeneous case inhomogeneous case absorbing inhomogeneity at 180˚

homogeneous phantom propagation of photon density and normalized maximum maximum moves to the center of the phantom

homogeneous phantom still images at 0.1, 0.2, 1, 2, 4, 5 ns maximum moves to the center of the phantom

inhomogeneous phantom propagation of photon density and normalized maximum absorbing inhomogeniety at 135˚ maximum moves to the center and then to the bottom left part of the phantom

inhomogeneous phantom absorbing inhomogeniety at 135˚ still images at 0.1, 0.5, 1, 2, 3 ns maximum moves to the center and then to the bottom left part of the phantom

scattering inhomogeniety at 135˚ inhomogeneous phantom propagation of photon density and normalized maximum maximum moves to the center and then to the upper right part of the phantom

inhomogeneous phantom scattering inhomogeniety at 135˚ still images at 0.1, 0.5, 1, 3, 5, 8 ns maximum moves to the center and then to the upper right part of the phantom

Inhomogeneity detection Cartesian coordinate system We obtain information from the tail of the time point spread function (TPSF) corresponding to the late arriving photons (LAP) and visualize it in three-dimensional surface. in Cartesian frame homogenous case TPSF converge to a plane in the inhomogeneous case, the curves also form a plane, but with a crevasse near position of the inhomogeneity.

Cartesian coordinate system Three-dimensional representation of TPSF for homogeneous (А) and inhomogeneous (В) cases Slide 12 (А) (В)

Conformal mapping to cylindrical coordinates system Using cylindrical system of coordinates in the homogenous case, TPSF are represented by a right cylindrical or corner surface. In the inhomogeneous case, conformal mapping shows a convexity near the angle where heterogeneity is located. Such 3D mapping provides quick real time detection of inhomogeneities without inverse problem solution.

Cylindrical coordinate system Three-dimensional conformal mapping of TPFS for homogeneous (А) and inhomogeneous (В) cases (А) (В)

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