PDE-constrained multispectral imaging of tissue chromophores with the equation of radiative transfer

Abstract

We introduce a transport-theory-based PDE-constrained multispectral model for direct imaging of the spatial distributions of chromophores concentrations in biological tissue. The method solves the forward problem (boundary radiance at each wavelength) and the inverse problem (spatial distribution of chromophores concentrations), in an all-at-once manner in the framework of a reduced Hessian sequential quadratic programming method. To illustrate the code’s performance, we present numerical and experimental studies involving tumor bearing mice. It is shown that the PDE-constrained multispectral method accelerates the reconstruction process by up to 15 times compared to unconstrained reconstruction algorithms and provides more accurate results as compared to the so-called two-step approach to multi-wavelength imaging.

A wireless handheld probe with spectrally constrained evolution strategies for diffuse optical imaging of tissue

“…To reconstruct the absolute values of absorption and scattering parameters in the medium, we normalized the target measurement data to a reference medium with known optical properties. 29 Measurements were made at the surface of an 8 cm × 8 cm × 8 cm box filled with 500 ml of 30 different solutions. Each solution consisted of an aqueous mixture made up of Intralipid R (Baxter Intralipid R 20% Fat Emulsion), black ink (Higgins India Ink), and near-infrared dye (Epolight TM 2735, Epolin Inc.).…”

“…The greatest value of the direct approach lies in the fact that it enables using all wavelengths data simultaneously to recover the parameters C i , A, and b which are wavelength independent, thereby making improvements to the non-uniqueness problem of diffuse optical imaging. [28][29][30][31] In this work, we make use of these benefits of the direct approach for spatially resolved spectroscopy (SRS) where bulk optical properties are to be obtained for a semi-infinite medium. The SRS problem with the direct approach can be formulated as the following inverse problem where the optimal solution can be found by minimizing the misfit between predictions R d and measurements z d of the reflectance on the tissue surface…”

Decoupled fluorescence Monte Carlo model for direct computation of fluorescence in turbid media

“…This is because the dfMC model is directly derived from the RTEs. [11][12] Also, the dfMC ensures that the fluorescence statistical quantities are unbiased, which means that the dfMC model can be as accurate as the RTEs if there are sufficient simulated photons. The discrepancies between the dfMC simulations and measurements mainly arise from statistical and measurement noise.…”

“…The present models for the excitation-to-emission conversion and the transport of the fluorescence in turbid media are derived from the radiative transport equations (RTEs), 11,12 including the simple analytical model, 13 diffusion approximation model, [14][15][16][17][18][19] and Monte Carlo (MC) model. [20][21][22][23][24][25][26][27] The analytical model can be applied only in relatively simple configurations, such as the slab model with homogeneous media.…”

Digital optical tomography system for dynamic breast imaging

“…40 In the following, we provide a brief description of this method, including the diffusion approximation as a light propagation model and the PDE-constrained inverse model of directly recovering chromophore concentrations in tissue.…”