The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach

Abstract

Near-infrared (NIR) tomography is a technique used to measure light propagation through tissue and generate images of internal optical property distributions from boundary measurements. Most popular applications have concentrated on female breast imaging, neonatal and adult head imaging, as well as muscle and small animal studies. In most instances a highly scattering medium with a homogeneous refractive index is assumed throughout the imaging domain. Using these assumptions, it is possible to simplify the model to the diffusion approximation. However, biological tissue contains regions of varying optical absorption and scatter, as well as varying refractive index. In this work, we introduce an internal boundary constraint in the finite element method approach to modelling light propagation through tissue that accounts for regions of different refractive indices. We have compared the results to data from a Monte Carlo simulation and show that for a simple two-layered slab model of varying refractive index, the phase of the measured reflectance data is significantly altered by the variation in internal refractive index, whereas the amplitude data are affected only slightly.

Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm

“…In frequency-domain DOT, [21][22][23][24][25][26][27][28][29] an iterative reconstruction approach is usually adopted to obtain the updated optical parameters using X = J T ͑JJ T + ␣H max I͒ −1 Y, where I is the identity matrix; H max is the maximum main diagonal elements of the matrix JJ T ; ␣ is the regularization parameter; and J is the Jacobian matrix for the inverse problem, which maps the changes in log amplitude and phase induced by changes in the absorption and reduced scattering coefficients. 23,25 The simulated case started with a 2-D 8.6-cm-diameter circular region ͑to mimic a breast cancer imager͒; the absorption and reduced scattering coefficients of this region were a = 0.1cm −1 and s Ј=10cm −1 , respectively.…”

Numerical modelling and image reconstruction in diffuse optical tomography

“…The air-tissue boundary is represented by an index-mismatched type III condition (also known as Robin or mixed boundary condition), in which the fluence at the edge of the tissue exits but does not return (Schweiger et al 1995;Dehghani et al 2003b). The flux leaving the external boundary is equal to the fluence rate at the boundary weighted by a factor that accounts for the internal reflection of light back into the tissue.…”

“…But, perhaps the most promising reason for adoption of numerical approaches is to facilitate the combination of NIR tomography with standard clinical imaging systems, using predefined tissue geometries as the input domain. A number of different numerical models have been developed and used with specific application in DOT, including finite elements (Arridge et al 1993;Jiang & Paulsen 1995;Schweiger et al 1995;Gao et al 1998;Jiang 1998;Dehghani et al 2003b), finite difference (Hielscher et al 1998;, finite volume (Ren et al 2004) and boundary elements (Zacharopoulos et al 2006;Srinivasan et al 2007). …”

Topology Optimization Using Hyper Radial Basis Function Network

“…Method that derives and linearizes the inverse problem to a well-posed boundary value problem for a coupled system of elliptic partial differential equations. Brian Pogue et al [49,50] have reconstructed images solving the inverse problem using the Levenberg-Marquardt optimization scheme. Yong Xu et al [51] have used regularized Newton approach to optimize the inverse problem objective function.…”