TRINITY: a three-dimensional time-dependent radiative transfer code for in-vivo near-infrared imaging

We develop a new three-dimensional time-dependent radiative transfer code, TRINITY (Time-dependent Radiative transfer In Near-Infrared TomographY), for in-vivo diffuse optical tomography (DOT). The simulation code is based on the design of long radiation rays connecting boundaries of a computational domain, which allows us to calculate light propagation with little numerical diffusion. We parallelize the code with Message Passing Interface (MPI) using the domain decomposition technique and confirm the high parallelization efficiency, so that simulations with a spatial resolution of $\sim 1$ millimeter can be performed in practical time. As a first application, we study the light propagation for a pulse collimated within $\theta \sim 15^\circ$ in a phantom, which is a uniform medium made of polyurethane mimicking biological tissue. We show that the pulse spreads in all forward directions over $\sim$ a few millimeters due to the multiple scattering process of photons. Our simulations successfully reproduce the time-resolved signals measured with eight detectors for the phantom. We also introduce the effects of reflection and refraction at the boundary of medium with a different refractive index and demonstrate the faster propagation of photons in an air hole that is an analogue for the respiratory tract.