Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation

As a molecular imaging technique, bioluminescence tomography (BLT) with its highly sensitive detection and facile operation can significantly reveal molecular and cellular information in vivo at the whole-body small animal level. However, because of complex photon transportation in biological tissue and boundary detection data with high noise, bioluminescent sources in deeper positions generally cannot be localized. In our previous work, we used achromatic or monochromatic measurements and an a priori permissible source region strategy to develop a multilevel adaptive finite-element algorithm. In this paper, we propose a spectrally solved tomographic algorithm with a posteriori permissible source region selection. Multispectral measurements, and anatomical and optical information first deal with the nonuniqueness of BLT and constrain the possible solution of source reconstruction. The use of adaptive mesh refinement and permissible source region based on a posteriori measures not only avoids the dimension disaster arising from the multispectral measured data but also reduces the ill-posedness of BLT and therefore improves the reconstruction quality. Reconsideration of the optimization method and related modifications further enhance reconstruction robustness and efficiency. We also incorporate into the method some improvements for reducing computational burdens. Finally, using a whole-body virtual mouse phantom, we demonstrate the capability of the proposed BLT algorithm to reconstruct accurately bioluminescent sources in deeper positions. In terms of optical property errors and two sources of discernment in deeper positions, this BLT algorithm represents the unique predominance for BLT reconstruction.     

Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system

Inevitable discrepancies between the mouse tissue optical properties assumed by an experimenter and the actual physiological values may affect the tomographic localization of bioluminescent sources. In a previous work, the simplifying assumption of optically homogeneous tissues led to inaccurate localization of deep sources. Improved results may be obtained if a mouse anatomical map is provided by a high-resolution imaging modality and optical properties are assigned to segmented tissues. In this work, the feasibility of this approach was explored by simulating the effect of different magnitude optical property errors on the image formation process of a combined optical-PET system. Some comparisons were made with corresponding simulations using higher spatial resolution data that are typically attainable by CCD cameras. In addition, simulation results provided insights on some of the experimental conditions that could lead to poor localization of bioluminescent sources. They also provided a rough guide on how accurately tissue optical properties need to be known in order to achieve correct localization of point sources with increasing tissue depth under low background noise conditions.     

A hyperspectral fluorescence system for 3D in vivo optical imaging

In vivo optical instruments designed for small animal imaging generally measure the integrated light intensity across a broad band of wavelengths, or make measurements at a small number of selected wavelengths, and primarily use any spectral information to characterize and remove autofluorescence. We have developed a flexible hyperspectral imaging instrument to explore the use of spectral information to determine the 3D source location for in vivo fluorescence imaging applications. We hypothesize that the spectral distribution of the emitted fluorescence signal can be used to provide additional information to 3D reconstruction algorithms being developed for optical tomography. To test this hypothesis, we have designed and built an in vivo hyperspectral imaging system, which can acquire data from 400 to 1000 nm with 3 nm spectral resolution and which is flexible enough to allow the testing of a wide range of illumination and detection geometries. It also has the capability to generate a surface contour map of the animal for input into the reconstruction process. In this paper, we present the design of the system, demonstrate the depth dependence of the spectral signal in phantoms and show the ability to reconstruct 3D source locations using the spectral data in a simple phantom. We also characterize the basic performance of the imaging system.     

Bioluminescence imaging of point sources implanted in small animals post mortem: evaluation of a method for estimating source strength and depth

The performance of a simple approach for the in vivo reconstruction of bioluminescent point sources in small animals was evaluated. The method uses the diffusion approximation as a forward model of light propagation from a point source in a homogeneous tissue to find the source depth and power. The optical properties of the tissue are estimated from reflectance images obtained at the same location on the animal. It was possible to localize point sources implanted in mice, 2-8 mm deep, to within 1 mm. The same performance was achieved for sources implanted in rat abdomens when the effects of tissue surface curvature were eliminated. The source power was reconstructed within a factor of 2 of the true power for the given range of depths, even though the apparent brightness of the source varied by several orders of magnitude. The study also showed that reconstructions using optical properties measured in situ were superior to those based on data in the literature.     

Boundary integral method for bioluminescence tomography

Bioluminescence tomography (BLT) allows in vivo localization and quantification of bioluminescent sources inside a small animal to reveal various molecular and cellular activities. We develop a reconstruction method to identify such a bioluminescent source distribution using the boundary integral method. Based on the diffusion model of the photon propagation in the biological tissue, this method incorporates a priori knowledge to define the permissible source region, and establish a direct linear relationship between measured body surface data and an unknown bioluminescent source distribution to enhance numerical stability and efficiency. The feasibility of the proposed BLT algorithm is demonstrated in heterogeneous mouse chest phantom studies.     

Excitation-resolved fluorescence tomography with simplified spherical harmonics equations

Fluorescence tomography (FT) reconstructs the three-dimensional (3D) fluorescent reporter probe distribution inside biological tissue. These probes target molecules of biological function, e.g. cell surface receptors or enzymes, and emit fluorescence light upon illumination with an external light source. The fluorescence light is detected on the tissue surface and a source reconstruction algorithm based on the simplified spherical harmonics (SP(N)) equations calculates the unknown 3D probe distribution inside tissue. While current FT approaches require multiple external sources at a defined wavelength range, the proposed FT method uses only a white light source with tunable wavelength selection for fluorescence stimulation and further exploits the spectral dependence of tissue absorption for the purpose of 3D tomographic reconstruction. We will show the feasibility of the proposed hyperspectral excitation-resolved fluorescence tomography method with experimental data. In addition, we will demonstrate the performance and limitations of such a method under ideal and controlled conditions by means of a digital mouse model and synthetic measurement data. Moreover, we will address issues regarding the required amount of wavelength intervals for fluorescent source reconstruction. We will explore the impact of assumed spatially uniform and nonuniform optical parameter maps on the accuracy of the fluorescence source reconstruction. Last, we propose a spectral re-scaling method for overcoming the observed limitations in reconstructing accurate source distributions in optically non-uniform tissue when assuming only uniform optical property maps for the source reconstruction process.     

A born-type approximation method for bioluminescence tomography

In this paper, we present a Born-type approximation method for bioluminescence tomography (BLT), which is to reconstruct an internal bioluminescent source from the measured bioluminescent signal on the external surface of a small animal. Based on the diffusion approximation for the photon propagation in biological tissue, this BLT method utilizes the Green function to establish a linear relationship between the measured bioluminescent signal and the internal bioluminescent source distribution. The Green function can be modified to describe a heterogeneous medium with an arbitrary boundary using the Born approximation. The BLT reconstruction is formulated in a linear least-squares optimization framework with simple bounds constraint. The performance of this method is evaluated in numerical simulation and phantom experiments.     

Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging

A new method is described for obtaining a 3-D reconstruction of a bioluminescent light source distribution inside a living animal subject, from multispectral images of the surface light emission acquired on charge-coupled device (CCD) camera. The method uses the 3-D surface topography of the animal, which is obtained from a structured light illumination technique. The forward model of photon transport is based on the diffusion approximation in homogeneous tissue with a local planar boundary approximation for each mesh element, allowing rapid calculation of the forward Green's function kernel. Absorption and scattering properties of tissue are measured a priori as input to the algorithm. By using multispectral images, 3-D reconstructions of luminescent sources can be derived from images acquired from only a single view. As a demonstration, the reconstruction technique is applied to determine the location and brightness of a source embedded in a homogeneous phantom subject in the shape of a mouse. The technique is then evaluated with real mouse models in which calibrated sources are implanted at known locations within living tissue. Finally, reconstructions are demonstrated in a PC3M-luc (prostate tumor line) metastatic tumor model in nude mice.     

Towards an inline reconstruction architecture for micro-CT systems

Recent developments in micro-CT have revolutionized the ability to examine in vivo living experimental animal models such as mouse with a spatial resolution less than 50 microm. The main requirements of in vivo imaging for biological researchers are a good spatial resolution, a low dose induced to the animal during the full examination and a reduced acquisition and reconstruction time for screening purposes. We introduce inline acquisition and reconstruction architecture to obtain in real time the 3D attenuation map of the animal fulfilling the three previous requirements. The micro-CT system is based on commercially available x-ray detector and micro-focus x-ray source. The reconstruction architecture is based on a cluster of PCs where a dedicated communication scheme combining serial and parallel treatments is implemented. In order to obtain high performance transmission rate between the detector and the reconstruction architecture, a dedicated data acquisition system is also developed. With the proposed solution, the time required to filter and backproject a projection of 2048 x 2048 pixels inside a volume of 140 mega voxels using the Feldkamp algorithm is similar to 500 ms, the time needed to acquire the same projection.     

Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study

The feasibility and limits in performing tomographic bioluminescence imaging with a combined optical-PET (OPET) system were explored by simulating its image formation process. A micro-MRI based virtual mouse phantom was assigned appropriate tissue optical properties to each of its segmented internal organs at wavelengths spanning the emission spectrum of the firefly luciferase at 37 degrees C. The TOAST finite-element code was employed to simulate the diffuse transport of photons emitted from bioluminescence sources in the mouse. OPET measurements were simulated for single-point, two-point and distributed bioluminescence sources located in different organs such as the liver, the kidneys and the gut. An expectation maximization code was employed to recover the intensity and location of these simulated sources. It was found that spectrally resolved measurements were necessary in order to perform tomographic bioluminescence imaging. The true location of emission sources could be recovered if the mouse background optical properties were known a priori. The assumption of a homogeneous optical property background proved inadequate for describing photon transport in optically heterogeneous tissues and led to inaccurate source localization in the reconstructed images. The simulation results pointed out specific methodological challenges that need to be addressed before a practical implementation of OPET-based bioluminescence tomography is achieved.     

Quantitative Evaluation of Bioluminescence Imaging Based on Radiative Transfer Equation

Bioluminescence imaging is a kind of emerging detection technology at cellular,molecular and genetic level.The most popular bioluminescence imaging model is diffusion approximation(DA).However,because of the ill-posedness of the DA-based inverse problem and the instability of reconstruction algorithms,the location accuracy of the reconstructed sources is low.Radiative transfer equation(RTE),which considers the direction of the photon migration and the effect of absorption and scattering in tissues,can accurately express the transmission of bioluminescent photons through the tissues.In this paper,we studied the bioluminescence imaging based on the RTE.2D simulations were performed,and quantitative evaluation was given by the absolute source position error,the relative source area error and the minimum bounding box.The results of the experiment showed that the imaging quality based on RTE was better than that one based on DA.     

Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography

We investigate fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography for applications in small animal imaging. Our forward model uses a diffusion approximation for optically inhomogeneous tissue, which we solve using a finite element method (FEM). We examine two approaches to incorporating the forward model into the solution of the inverse problem. In a conventional direct calculation approach one computes the full forward model by repeated solution of the FEM problem, once for each potential source location. We describe an alternative on-the-fly approach where one does not explicitly solve for the full forward model. Instead, the solution to the forward problem is included implicitly in the formulation of the inverse problem, and the FEM problem is solved at each iteration for the current image estimate. We evaluate the convergence speeds of several representative iterative algorithms. We compare the computation cost of those two approaches, concluding that the on-the-fly approach can lead to substantial reductions in total cost when combined with a rapidly converging iterative algorithm.     

Cone-beam x-ray microtomography of small specimens

Microtomography is a technique for creating three-dimensional images of the internal structure of objects with high spatial resolution. This can potentially allow inspection of the architecture of breast lumpectomy specimens and visualization of tumours in small animals and also has an application as a tool for non-destructive testing. An efficient method to perform microtomography is to use an area detector and cone-beam reconstruction techniques. In this paper we report on the development of an instrument for microtomography and show example images. The equipment consists of a microfocal x-ray tube (energies and currents up to 30 kVp, 0.2 mA, focal spot size < 5 microm), a rotating specimen stage and a high-resolution x-ray image intensifier optically coupled to a CCD video camera. Data acquisition and 3D image reconstruction are performed by a desktop computer. The well-known Feldkamp cone-beam reconstruction algorithm is used to produce tomographic images from the recorded x-ray projections. The instrument can image samples with diameters of 5-50 mm and create tomographic images with spatial resolution of the order 10-100 microm and signal-to-noise ratio of better than 5:1. This work is a continuation and improvement of an earlier instrument with a low-energy x-ray source and detector.     

Spatio-temporal Reconstruction of Neural Sources Using Indirect Dominant Mode Rejection

Adaptive minimum variance based beamformers (MVB) have been successfully applied to magnetoencephalogram (MEG) and electroencephalogram (EEG) data to localize brain activities. However, the performance of these beamformers falls down in situations where correlated or interference sources exist. To overcome this problem, we propose indirect dominant mode rejection (iDMR) beamformer application in brain source localization. This method by modifying measurement covariance matrix makes MVB applicable in source localization in the presence of correlated and interference sources. Numerical results on both EEG and MEG data demonstrate that presented approach accurately reconstructs time courses of active sources and localizes those sources with high spatial resolution. In addition, the results of real AEF data show the good performance of iDMR in empirical situations. Hence, iDMR can be reliably used for brain source localization especially when there are correlated and interference sources.     

Optical tomographic mapping of cerebral haemodynamics by means of time-domain detection: methodology and phantom validation

One of the primary applications of diffuse optical imaging is to localize and quantify the changes in the cerebral oxygenation during functional brain activation. Up to now, data from an optical imager are simply presented as a two-dimensional (2D) topographic map using the modified Beer-Lambert law that assumes homogeneous optical properties beneath each optode. Due to the highly heterogeneous nature of the optical properties in the brain, the assumption is evidently invalid, leading to both low spatial resolution and inaccurate quantification in the assessment of haemodynamic changes. To cope with these difficulties, we propose a nonlinear tomographic image reconstruction algorithm for a two-layered slab geometry that uses time-resolved reflected light. The algorithm is based on the previously developed generalized pulse spectrum technique, and implemented within a semi-three-dimensional (3D) framework to conform to the topographic visualization and to reduce computational load. We demonstrate the advantages of the algorithm in quantifying simulated changes in haemoglobin concentrations and investigate its robustness to the uncertainties in the cortical structure and optical properties, as well as the effects of random noises on image quality. The methodology is also validated by experiments using a solid layered phantom.     

Combined magnetic resonance and bioluminescence imaging of live mice

We perform combined magnetic resonance and bioluminescence imaging of live mice for the purpose of improving the accuracy of bioluminescence tomography. The imaging is performed on three live nude mice in which tritium-powered light sources are surgically implanted. High-resolution magnetic resonance images and multispectral, multiview bioluminescence images are acquired in the same session. An anatomical model is constructed by segmenting the magnetic resonance images for all major tissues. The model is subsequently registered with nonlinear transformations to the 3-D light exittance (exiting intensity) surface map generated from the luminescence images. A Monte Carlo algorithm, along with a set of tissue optical properties obtained from in vivo measurements, is used to solve the forward problem. The measured and simulated light exittance images are found to differ by a factor of up to 2. The greatest cause of this moderate discrepancy is traced to the small errors in source positioning, and to a lesser extent to the optical properties used for the tissues. Discarding the anatomy and using a homogeneous model leads to a marginally worse agreement between the simulated and measured data.     

Accurate localization of intracavitary brachytherapy applicators from 3D CT imaging studies

PURPOSE: To present an accurate method to identify the positions and orientations of intracavitary (ICT) brachytherapy applicators imaged in 3D CT scans, in support of Monte Carlo photon-transport simulations, enabling accurate dose modeling in the presence of applicator shielding and interapplicator attenuation. MATERIALS AND METHODS: The method consists of finding the transformation that maximizes the coincidence between the known 3D shapes of each applicator component (colpostats and tandem) with the volume defined by contours of the corresponding surface on each CT slice. We use this technique to localize Fletcher-Suit CT-compatible applicators for three cervix cancer patients using post-implant CT examinations (3 mm slice thickness and separation). Dose distributions in 1-to-1 registration with the underlying CT anatomy are derived from 3D Monte Carlo photon-transport simulations incorporating each applicator's internal geometry (source encapsulation, high-density shields, and applicator body) oriented in relation to the dose matrix according to the measured localization transformations. The precision and accuracy of our localization method are assessed using CT scans, in which the positions and orientations of dense rods and spheres (in a precision-machined phantom) were measured at various orientations relative to the gantry. RESULTS: Using this method, we register 3D Monte Carlo dose calculations directly onto post insertion patient CT studies. Using CT studies of a precisely machined phantom, the absolute accuracy of the method was found to be +/-0.2 mm in plane, and +/-0.3 mm in the axial direction while its precision was +/-0.2 mm in plane, and +/-0.2 mm axially. CONCLUSION: We have developed a novel, and accurate technique to localize intracavitary brachytherapy applicators in 3D CT imaging studies, which supports 3D dose planning involving detailed 3D Monte Carlo dose calculations, modeling source positions, shielding and interapplicator shielding, accurately.     

Real time noninvasive monitoring of contaminating bacteria in a soft tissue implant infection model

Infection is the main cause of biomaterials-related failure. A simple technique to test in-vivo new antimicrobial and/or nonadhesive implant coatings is unavailable. Current in vitro methods for studying bacterial adhesion and growth on biomaterial surfaces lack the influence of the host immune system. Most in vivo methods to study biomaterials-related infections routinely involve implant-removal, preventing comprehensive longitudinal monitoring. In vivo imaging circumvents these drawbacks and is based on the use of noninvasive optical imaging of bioluminescent bacteria. Staphylococcus aureus Xen29 is genetically modified to be stably bioluminescent, by the introduction of a modified full lux operon onto its chromosome. Surgical meshes with adhering S. aureus Xen29 were implanted in mice and bacterial growth and spread into the surrounding tissue was monitored longitudinally from bioluminescence with a highly sensitive CCD camera. Distinct spatiotemporal bioluminescence patterns, extending beyond the mesh area into surrounding tissues were observed. After 10 days, the number of living organisms isolated from explanted meshes was found to correlate with bioluminescence prior to sacrifice of the animals. Therefore, it is concluded that in vivo imaging using bioluminescent bacteria is ideally suited to study antimicrobial coatings taking into account the host immune system. In addition, longitudinal monitoring of infection in one animal will significantly reduce the number of experiments and animals.     

Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models

Generally, the performance of tomographic bioluminescence imaging is dependent on several factors, such as regularization parameters and initial guess of source distribution. In this paper, a global-inexact-Newton based reconstruction method, which is regularized by a dynamic sparse term, is presented for tomographic reconstruction. The proposed method can enhance higher imaging reliability and efficiency. In vivo mouse experimental reconstructions were performed to validate the proposed method. Reconstruction comparisons of the proposed method with other methods demonstrate the applicability on an entire region. Moreover, the reliable performance on a wide range of regularization parameters and initial unknown values were also investigated. Based on the in vivo experiment and a mouse atlas, the tolerance for optical property mismatch was evaluated with optical overestimation and underestimation. Additionally, the reconstruction efficiency was also investigated with different sizes of mouse grids. We showed that this method was reliable for tomographic bioluminescence imaging in practical mouse experimental applications.     

Limited-angle 3D reconstruction of PET images for dose localization in light ion tumour therapy.

In vivo dose localization in light ion tumour therapy can be performed by measuring the range distributions of beta+ active ions in tissue employing positron emission tomographic techniques. For this purpose a multiplicative iteration scheme for reconstructing three-dimensional images from shift-variant, limited-angle data is presented. In the iterative correction steps the algorithm uses the geometric means of quotients calculated from the three-dimensional Radon transforms of the backprojected measured and approximated source distributions. When sources measured with poor statistics are reconstructed, an effective noise suppression is achieved.