Abstract
The forward model in diffuse optical tomography (DOT) describes how light propagates through a turbid medium. It is often approximated by a diffusion equation (DE) that is numerically discretized by the classical finite element method (FEM). We propose a nonlocal diffusion equation (NDE) as a new forward model for DOT, the discretization of which is carried out with an efficient graph-based numerical method (GNM). To quantitatively evaluate the new forward model, we first conduct experiments on a homogeneous slab, where the numerical accuracy of both NDE and DE is compared against the existing analytical solution. We further evaluate NDE by comparing its image reconstruction performance (inverse problem) to that of DE. Our experiments show that NDE is quantitatively comparable to DE and is up to 64% faster due to the efficient graph-based representation that can be implemented identically for geometries in different dimensions. The proposed discretization method can be easily applied to other imaging techniques like diffuse correlation spectroscopy which are normally modeled by the diffusion equation.
Highlights
In diffuse optical tomography (DOT), near-infrared light (650-900 nm) is injected into an object through optical fibers placed on its surface
The nonlocal diffusion equation (NDE) method with the graph-based numerical method (GNM) implementation will be compared against the original diffusion equation (DE) with the finite element method (FEM) implementation
For the forward model based on FEM, such a discrete structure can be directly employed for the finite element method
Summary
In diffuse optical tomography (DOT), near-infrared light (650-900 nm) is injected into an object through optical fibers placed on its surface. The forward model of light propagation must be able to accurately model the main interactions (i.e. absorption and scattering) between light and the object so as to recover internal properties faithfully. When its wave nature is neglected and light is interpreted as a stream of particles (photons), the main interactions between light and biological tissue are characterized as absorption and scattering and are modelled by the radiative transfer equation (RTE) which is generally accepted to accurately describe how light propagates in biological tissues [1,2]. The Monte Carlo method is the most commonly used stochastic model [7,8] It is costly in computational time, because millions of photons need to be tracked to acquire meaningful statistics. Light propagation can be modelled by a deterministic diffusion equation (DE) using the P1 approximation of the RTE. Bhatt et al [12] proposed a generalized Beer–Lambert model to overcome this limitation and have applied this method widely to near-infrared spectroscopy (NIRS) studies
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