Radiative transfer of luminescence light in biological tissue

Abstract

We present the first algorithm for solving the equation of radiative transfer (ERT) in the frequency domain (FD) on three-dimensional block-structured Cartesian grids (BSG). This algorithm allows for accurate modeling of light propagation in media of arbitrary shape with air-tissue refractive index mismatch at the boundary at increased speed compared to currently available structured grid algorithms. To accurately model arbitrarily shaped geometries the algorithm generates BSGs that are finely discretized only near physical boundaries and therefore less dense than fine grids. We discretize the FD-ERT using a combination of the upwind-step method and the discrete ordinates (S N) approximation. The source iteration technique is used to obtain the solution. We implement a first order interpolation scheme when traversing between coarse and fine grid regions. Effects of geometry and optical parameters on algorithm performance are evaluated using numerical phantoms (circular, cylindrical, and arbitrary shape) and varying the absorption and scattering coefficients, modulation frequency, and refractive index. The solution on a 3-level BSG is obtained up to 4.2 times faster than the solution on a single fine grid, with minimal increase in numerical error (less than 5%).

Concurrent visualization of trafficking, expansion, and activation of T lymphocytes and T-cell precursors in vivo

“…We acquired bioluminescence data in a manner suitable for tomographic reconstruction and calculated the 3D distribution of the NFAT-activation signal. 12 The result clearly showed a localization of activated cells in the region of the thymus ( Figure 6B), which was confirmed by subsequent ex vivo measurements.…”

“…The light propagation within the mouse was calculated using a Simplified Spherical Harmonics (specifically the SP 3 ) solution to the radiative transfer model. 12 These solutions have been shown to be more accurate for small geometries (such as a mouse) and short wavelengths (Ͻ 600 nm) than the more simplistic and commonly used diffusion model.…”

Computer-aided diagnosis of rheumatoid arthritis with optical tomography, Part 1: feature extraction

“…Furthermore, potential artifacts introduced by boundary effects are minimal. 32,33 The center of the joint is at the geometrical center of the imaged finger, whose dimensions we know from the imaging procedure where the geometry of each finger is captured. Subsequently, we use this geometry to generate the FVM on which we compute the forward and inverse DOT problems.…”

Implementation of the radiative transfer equation on block-structured grids for modeling fluorescence light propagation in tissue with arbitrary shape

“…1 Time domain systems typically pose the most difficulty from an experimental point of view. The steady state domain problem has been shown to be highly ill posed and thus of limited use.…”

“…4 The frequency domain ERT has received much attention over the past decade. 1,7,15,16,17 Often, the numerical schemes used to solve the ERT include a combination of discrete ordinates for the angular variable and either a finite differences, finite volume, or finite element method for the spatial variable. 1,12,3,7,10,11,16,17 The most common type of differencing scheme for the spatial variable is the step method.…”