Optical imaging techniques have long been popular for generating contrast representing molecular processes in tissue. Over the past decade, their applications have extended from microscopy to macroscopic imaging of deep-tissue optical sources by exploiting the near-infrared (NIR) window where water, oxyhemoglobin, and deoxyhemoglobin, the primary absorbers in tissue, have relatively low absorption coefficients allowing light to penetrate several centimeters inside tissue (Weissleder and Ntziachristos 2003
). The non-ionizing nature of NIR light, the availability of a variety of highly specific fluorescent probes, and, finally, low cost offer these methods some leverage over existing radiological techniques for molecular imaging (Hebden et al 1997
). However, penetration depths of only a few centimeters are insufficient for most clinical deep-tissue imaging applications. Thus the success of 3D optical imaging methods in clinical diagnostics is restricted to only a few applications. These include NIR spectroscopy and diffuse optical tomography used for mapping brain structure and function in neonates (Koizumi et al 2003
, Villringer and Chance 1997
, Hebden et al 2002
) and optical mammography for breast cancer screening (Ntziachristos and Chance 2001
, Culver et al 2003
). Optical tomographic methods show great promise in preclinical research, which is a valuable translational tool between in vitro
studies and clinical applications. Fluorescence molecular tomography (FMT) and bioluminescence tomography (BLT) have emerged as promising low-cost alternatives to PET and SPECT for functional imaging in small animals, thus greatly impacting diagnostics, drug discovery, and therapeutics (Ntziachristos et al 2005
, Gibson et al 2005
). Although plagued by tissue autofluorescence, FMT has many advantages over BLT. Compared to most bioluminescent probes, commonly used fluorophores emit light at longer wavelengths (where tissues are less absorbing) consequently offering higher detected signal strengths (Contag and Bachmann 2002
, Hielscher 2005
). Additionally multiple illumination patterns can be used to generate different mappings from the source space to the detector space making the FMT problem less ill-posed than the BLT problem (Chaudhari et al 2005
). The success of FMT can be attributed to a number of breakthroughs.
- The availability of a variety of new NIR fluorescent dyes, active or activatable fluorescent biomarkers, and fluorescent proteins expressed by reporter genes has enabled visualization of gene expression and several cellular and subcellular processes in vivo (Massoud and Gambhir 2003, Shu et al 2009).
- Advances in instrumentation have led to the development of a range of imaging systems for time-domain, frequency-domain, and continuous-wave (CW) FMT (Kumar et al 2008, Godavarty et al 2005, Zavattini et al 2006). Some of the newer systems feature non-contact tomographic detection using CCD cameras with free-space detection geometries and/or innovative optics for full-surface visualization, thus eliminating the need for optical fibers and matching fluids (Li et al 2009, Graves et al 2003, Patwardhan et al 2005).
- Finally, a number of theoretical and computational advances have led to the development of realistic forward models and robust inverse methods. Popular methods employed to model photon propagation through tissue for solving the forward problem include Monte Carlo methods (Hayakawa et al 2001, Boas et al 2002, Chen and Intes 2009) as well as analytical and numerical solutions to the radiative transport equation (Klose et al 2002) and the diffusion equation (Rice et al 2001, Dutta et al 2008, Arridge et al 1993) subject to different boundary conditions (Haskell et al 1994). These forward modeling schemes coupled with fast inversion techniques (Roy and Sevick-Muraca 2001, Ahn et al 2008, Zacharopoulos et al 2009) have made it feasible to reconstruct FMT images accurately and efficiently.
Despite their tremendous potential and increasing popularity, fluorescence tomographic techniques are confounded by high degrees of absorption and scattering of photons propagating through tissue, making the FMT problem ill-posed. One approach for alleviating this problem and improving source localization is to harness spectral variations of tissue optical properties by using multispectral illumination and/
or detection (Zacharakis et al 2005
, Chaudhari et al 2009
). Another approach is to exploit the degree of freedom offered by external illumination in FMT and design a set of spatial illumination patterns that improve the conditioning of the forward model matrix (Dutta et al 2009
), and that is the focus of this paper.
FMT setups typically acquire data-sets corresponding to different surface illumination patterns. These patterns generate different excitation fields over the volume, which tune the system matrix. FMT setups available today employ illumination schemes chiefly guided by the availability and simplicity of the light source. Several of these use laser sources with focusing or diffuser lenses to generate point or distributed patch patterns (Graves et al 2003
, Zavattini et al 2006
, Li et al 2009
). Other approaches include raster scanning (Patwardhan et al 2005
, Joshi et al 2006
) and structured light or spatially modulated illumination patterns (Lukic et al 2009
). Most of these approaches are ad hoc. Although various performance metrics could be used to theoretically compare these standard approaches, it is impossible to make an exhaustive set of comparisons, since, for a given number of illumination patterns being used for an experiment, infinitely many designs exist. Therefore, the question we address in this paper is as follows: given a fixed number of illumination patterns, how do we design these patterns so as to maximize the information in the acquired data?
With the availability of Texas Instruments Digital Light Processor (DLP®
) chips (Hornbeck 1996
, Dudley et al 2003
) which work in the near-infrared range and give us precise control over the spatial intensity distribution, it is feasible to generate any set of spatial illumination patterns with grayscale intensity variation (Gardner et al 2010
, Bassi et al 2008
, Konecky et al 2009
, Bélanger et al 2010
). The focus of this paper is to compute the set of illumination patterns for CW FMT that maximize the information content in the data by improving the conditioning of the Fisher information matrix. We formulate our problem as a constrained optimization problem that minimizes a cost function derived from the Fisher information matrix and computes the parameterized set of optimal spatial patterns.
Section 2 of this paper provides a description of the CW FMT problem. The formulation of the optimization problem that generates the optimal set of patterns is presented in section 3. In section 4, we describe the methods used to solve the forward and inverse problems, the optimization procedure, and the performance metrics used to evaluate different illumination schemes. Section 5 presents optimal patterns on a cylinder, a cuboidal tissue phantom, and a mouse atlas along with performance comparisons of illumination schemes for the atlas. Finally, a discussion of the results is presented in section 6.