Abstract: The use of the boundary element method (BEM) is explored as an alternative to the finite element method (FEM) solution methodology for the elliptic equations used to model the generation and transport of fluorescent light in highly scattering media, without the need for an internal volume mesh. The method is appropriate for domains where it is reasonable to assume the fluorescent properties are regionally homogeneous, such as when using highly specific molecularly targeted fluorescent contrast agents in biological tissues. In comparison to analytical results on a homogeneous sphere, BEM predictions of complex emission fluence are shown to be more accurate and stable than those of the FEM. Emission fluence predictions made with the BEM using a 708-node mesh, with roughly double the inter-node spacing of boundary nodes as in a 6956-node FEM mesh, match experimental frequency-domain fluorescence emission measurements acquired on a 1087 cm^3 breast-mimicking phantom at least as well as those of the FEM, but require only 1/8 to 1/2 the computation time.
Abstract: The use of the boundary element method is explored as an alternative solution methodology for the coupled elliptic equations used to model generation and transport of fluorescent light in highly scattering media.
Abstract: Many approaches to fluorescence tomography utilize some form of regularized nonlinear least-squares algorithm for data inversion, thus requiring repeated computation of the Jacobian sensitivity matrix relating changes in observable quantities, such as emission fluence, to changes in underlying optical parameters, such as fluorescence absorption. An exact adjoint formulation of these sensitivities comprises three terms, reflecting the individual contributions of 1) sensitivities of diffusion and decay coefficients at the emission wavelength, 2) sensitivities of diffusion and decay coefficients at the excitation wavelength, and 3) sensitivity of the emission source term. Simplifying linearity assumptions are computationally attractive in that they cause the first and second terms to drop out of the formulation. The relative importance of the three terms is thus explored in order to determine the extent to which these approximations introduce error. Computational experiments show that, while the third term of the sensitivity matrix has the largest magnitude, the second term becomes increasingly significant as target fluorophore concentration or volume increases. Image reconstructions from experimental data confirm that neglecting the second term results in overestimation of sensitivities and consequently overestimation of the value and volume of the fluorescent target, whereas contributions of the first term are so low that they are probably not worth the additional computational costs.
Abstract: We present a computationally efficient and accurate adjoint method for calculating coupled sensitivities of complex frequency-domain excitation and emission fluence to any underlying optical parameters in highly scattering media. The method is shown to be general and accurate. Novel vectorized implementations for finite element global matrix assembly and adjoint sensitivity calculations are shown to speed up calculations by orders of magnitude over traditional loop implementations, thereby making least-squares approaches to fluorescence tomography computationally practical.
Abstract: The adjoint sensitivity method is applied to the coupled partial differential equations approximating complex fluence in fluorescing system. General equations are derived for Jacobian sensitivity matrices of complex fluence, at both excitation and emission wavelengths, with respect to arbitrary optical parameters. Finite element implementations of these equations are found to be computationally efficient and accurate.