Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach.

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of "how well do we know our parameters, along with their uncertainties?.

Non-contact fluorescence optical tomography with scanning patterned illumination.

This article describes a novel non-contact fluorescence optical tomography scheme which utilizes multiple area illumination patterns, to reduce the ill-posedness of the inverse problem involved in recovering interior fluorescence yield distributions in biological tissue from boundary fluorescence measurements. The image reconstruction is posed as an optimization problem which seeks a tissue optical property distribution minimizing, for all illumination patterns simultaneously, a regularized difference between the observed boundary measurements of light distribution, and the boundary measurements predicted from a physical model. Multiple excitation source illumination patterns are described by line and Gaussian sources scanning the simulated tissue phantom surface and by employing diffractive optics-generated patterns.

Fully adaptive FEM based fluorescence optical tomography from time-dependent measurements with area illumination and detection.

Using an area-illumination and area-detection scheme, we acquire fluorescence frequency domain measurements from a tissue phantom with an embedded fluorescent target and obtain tomographic reconstructions of the interior fluorescence absorption map with an adaptive finite element based scheme. The tissue phantom consisted of a clear acrylic cubic box (512 ml) filled with 1% Liposyn solution, while the fluorescent targets were 5 mm diameter glass bulbs filled with 1 microM Indocyanine Green dye solution in 1% Liposyn. Frequency domain area illumination and detection employed a planar excitation source using an expanded intensity modulated (100 MHz) 785 nm diode laser light and a gain modulated image intensified charge coupled device camera, respectively.

Plane-wave fluorescence tomography with adaptive finite elements.

We present three-dimensional fluorescence yield tomography of a tissue phantom in a noncontact reflectance imaging setup. The method employs planar illumination with modulated light and frequency domain fluorescence measurements made on the illumination plane. An adaptive finite-element algorithm is used to handle the ill-posed and computationally demanding inverse image reconstruction problem.

Adaptive finite element based tomography for fluorescence optical imaging in tissue.

A three-dimensional fluorescence-enhanced optical tomography scheme based upon an adaptive finite element formulation is developed and employed to reconstruct fluorescent targets in turbid media from frequency-domain measurements made in reflectance geometry using area excitation illumination. The algorithm is derived within a Lagrangian framework by treating the photon diffusion model as a constraint to the optimization problem. Adaptively refined meshes are used to separately discretize maps of the forward/adjoint variables and the unknown parameter of fluorescent yield.