Optimization of 360° projection fluorescence molecular tomography

Abstract

Fluorescence tomography of tissues has been generally limited to systems that require fixed geometries or measurements employing fibers. Certain technological advances however, have more recently allowed the development of complete-projection 360° tomographic approaches using non-contact detection and illumination. Employing multiple illumination projections and CCD cameras as detection devices vastly increases the information content acquired, posing non-trivial computational and experimental requirements. In this paper, we use singular-value analysis to optimize experimental parameters relevant to the design and operation of emerging 360° fluorescence molecular tomography (FMT) methods and systems for small animal imaging. We present the theoretical and experimental methodology, optimization results and their experimental validation. We further discuss how these results can be employed to improve the performance of existing FMT systems and guide the design of new systems.

Introduction

Fluorescence molecular tomography (FMT) is a technique developed to overcome limitations of epi-illumination (photographic) fluorescence imaging and offers three-dimensional quantitative visualization of fluorescence bio-distribution in vivo in small animals (Ntziachristos et al., 2005). In the preferred implementation, FMT collects photons at the emission wavelength of fluorochromes distributed in tissues at multiple projections and combines these measurements tomographically with photons collected at the excitation wavelength to obtain fluorescence images of deep tissues. To achieve this, FMT typically employs a mathematical model of photon propagation in diffusive media and constructs a forward model which is then solved for the unknown fluorochrome bio-distribution. Typically, fluorochromes are extrinsically administered and can preferentially home in on tissues or cells of interest, although in principle tissue auto-fluorescence can be similarly distributed. With the potential to employ several engineered fluorochromes with specificity to various molecular processes (Achilefu, 2004, Bornhop et al., 2001, Tung, 2004) FMT can facilitate non-invasive macroscopic observations of cellular and sub-cellular function through entire animals. FMT has so far been applied to resolving tumor-related protease activity, responses to chemotherapy and angiogenesis (Ntziachristos et al., 2005) and is expected to find increasing further application to basic research and drug discovery.

Technologically, FMT is in its infancy. Original tomographic systems for small animal imaging utilized only a small number of measurements and often employed matching fluids for simplifying methodological and theoretical requirements, yielding images of compromised performance (Ntziachristos et al., 2002, Gurfinkel et al., 2003). Recently, systems that operate without the need to bring fibers in contact with tissue or to use matching media have simplified experimental procedures and produce superior imaging performance (Schultz et al., 2004). These new technologies now enable the implementation of complete projection 360° tomographic approaches using CCD cameras in non-contact detection mode and similarly non-contact illumination using appropriately oriented light beams (Turner et al., 2005). Such implementations are common to most other tomographic imaging modalities (for example PET and SPECT) and in particular in X-ray CT, which also utilizes an external energy source and a two-dimensional array of detectors for signal collection.

While 360° geometries using CCD cameras can maximize the information content available in the measurements, there has been little experience with such implementations for optical tomography applications through tissues. Cylindrical geometries have been implemented in the past for diffuse optical tomography applications (Pogue et al., 2001, Colak et al., 1999, Schmitz et al., 2002) and their benefit over other geometrical implementations has also been demonstrated (Pogue et al., 1999). However, these implementations considered sparse surface measurements, using a relatively small number of fibers placed symmetrically around the tissue boundary and in contact with the diffuse medium. Alternatively, slab geometry systems with direct CCD camera coupling have been considered, however such systems offered limited projection viewing (Culver et al., 2003, Patwardhan et al., 2005, Graves et al., 2003). Therefore, limited knowledge has been available on the optimal implementation of experimental parameters for developing and utilizing the data obtained with a CCD camera based 360° tomographic imaging system, i.e., a complete projection system offering high spatial sampling of photon patterns propagating through tissue.

An important consideration in the design of 360° CCD camera based systems is the vast amount of data that can be collected. An FMT system developed in our laboratory using this technology (Deliolanis et al., 2007) typically collects 10⁸–10¹⁰ measurements, when considering the size of a single CCD camera measurement (10⁶) further multiplied by the number of possible projections (10–100) and light sources utilized (10–100). In addition, FMT requires a theoretical model (the forward model) that predicts photon propagation from a given source position through a diffusive medium to a given detector position. In most common implementations today, this involves an approximation of the radiative transfer equation and yields a linear system m = Wn, where a weight matrix W couples the fluorochrome distribution n to the measurements m. This system is then solved for n by inverting the weight matrix W. The size of the weight matrix W is determined by the product of the number of measurements utilized and the number of voxels employed to discretize the fluorochrome distribution n in the volume of interest. For example, more than 2³² matrix elements need to be computed and stored even when using moderate sampling parameters, for example by using 7 × 7 sources, 20 × 20 detectors, a 20 × 20 × 20 discretization grid and 36 projections. It follows that such inversion problems can yield very high memory and computational requirements, which today’s computers cannot satisfy. This is particularly true when high spatial resolution and better image fidelity is pursued as this involves increasing the number of sources and detectors as well as the discretization step of the reconstruction grid. Therefore, optimization of experimental parameters which maximizes the information content of the acquired measurements, while minimizing the associated memory storage requirements and computational expense, is an important step towards achieving practical computation schemes. Besides the computational considerations, this optimization is equally important for minimizing acquisition times and suggesting optimal designs for hardware development.

Herein we therefore address several open questions as to the optimal design and operation of new potent FMT systems employing complete projection (360°) illumination and detection in constant wave (CW) mode, i.e., using illumination of constant intensity. We employ the singular-value analysis (SVA) (Culver et al., 2001) as a tool for analytically assessing optimal experimental parameters. The SVA has been previously employed in optimizing source/detector arrangements and the field of view in parallel plate geometries (Graves et al., 2004), for comparing parallel plate transmission and remission geometries (Culver et al., 2001) and for optimizing the placement of fibers for a hybrid magnetic resonance imaging/near infrared imaging device for small animal brain studies (Xu et al., 2003). SVA generically evaluates the relative performance of different parameter sets (for example the spatial sampling of sources and detectors, or the field of view employed), and can be used to draw generic conclusions on optimal parameter sets. Herein, we employed SVA to study the 360° geometry in two assumed systems; the first considering a parallel plate system that can freely rotate for implementing 360° projection capacity and the second implementing a free-space system also using 360° non-contact rotation as explained in methods. The difference between these two systems is that the first describes an approach where a mouse is rotated within a slab geometry containing a matching fluid, whereas the second system reflects an implementation whereas a mouse is rotated in the absence of matching fluid (free-space) or equally, whereas the optical system is rotated around a mouse. SVA analysis was confirmed with experimental data from two corresponding experimental setups. We were particularly interested in identifying the optimal number of projections that should be employed for small animal imaging and whether a fan bean vs. a scan beam illumination would be more appropriate for imaging purposes. In addition, we optimized the spatial sampling and the field of view for the sources, detectors and mesh points employed. In the following, we present the methods used in our analysis, the theoretical and experimental results obtained and discuss the major findings and the limitations of this study.