Spectrally resolved bioluminescence tomography using the reciprocity approach

Dictionary Learning Method Based on K-Sparse Approximation and Orthogonal Procrustes Analysis for Reconstruction in Bioluminescence Tomography

Bioluminescence tomography (BLT) is one kind of noninvasive optical molecular imaging technology, widely used to study molecular activities and disease progression inside live animals. By combining the optical propagation model and inversion algorithm, BLT enables three-dimensional imaging and quantitative analysis of light sources within organisms. However, challenges like light scattering and absorption in tissues, and the complexity of biological structures, significantly impact the accuracy of BLT reconstructions. Here, we propose a dictionary learning method based on K-sparse approximation and Orthogonal Procrustes analysis (KSAOPA). KSAOPA uses an iterative alternating optimization strategy, enhancing solution sparsity with k-coefficients Lipschitzian mappings for sparsity(K-LIMAPS) in the sparse coding stage, and reducing errors with Orthogonal Procrustes analysis in the dictionary update stage, leading to stable and precise reconstructions. We assessed the method performance through simulations and in vivo experiments, which showed that KSAOPA excels in localization accuracy, morphological recovery, and in vivo applicability compared to other methods.

Assessing the Accuracy of Bioluminescence Image-Guided Stereotactic Body Radiation Therapy of Orthotopic Pancreatic Tumors Using a Small Animal Irradiator

Stereotactic body radiation therapy (SBRT) has shown promising results in the treatment of pancreatic cancer and other solid tumors. However, wide adoption of SBRT remains limited largely due to uncertainty about the treatment's optimal fractionation schedules to elicit maximal tumor response while limiting the dose to adjacent structures. A small animal irradiator in combination with a clinically relevant oncological animal model could address these questions. Accurate delivery of X rays to animal tumors may be hampered by suboptimal image-guided targeting of the X-ray beam in vivo. Integration of bioluminescence imaging (BLI) into small animal irradiators in addition to standard cone-beam computed tomography (CBCT) imaging improves target identification and high-precision therapy delivery to deep tumors with poor soft tissue contrast, such as pancreatic tumors. Using bioluminescent BxPC3 pancreatic adenocarcinoma human cells grown orthotopically in mice, we examined the performance of a small animal irradiator equipped with both CBCT and BLI in delivering targeted, hypo-fractionated, multi-beam SBRT. Its targeting accuracy was compared with magnetic resonance imaging (MRI)-guided targeting based on co-registration between CBCT and corresponding sequential magnetic resonance scans, which offer greater soft tissue contrast compared with CT alone. Evaluation of our platform's BLI-guided targeting accuracy was performed by quantifying in vivo changes in bioluminescence signal after treatment as well as staining of ex vivo tissues with γH2AX, Ki67, TUNEL, CD31 and CD11b to assess SBRT treatment effects. Using our platform, we found that BLI-guided SBRT enabled more accurate delivery of X rays to the tumor resulting in greater cancer cell DNA damage and proliferation inhibition compared with MRI-guided SBRT. Furthermore, BLI-guided SBRT allowed higher animal throughput and was more cost effective to use in the preclinical setting than MRI-guided SBRT. Taken together, our preclinical platform could be employed in translational research of SBRT of pancreatic cancer.

Quantitative molecular bioluminescence tomography

SIGNIFICANCE

Bioluminescence imaging and tomography (BLT) are used to study biologically relevant activity, typically within a mouse model. A major limitation is that the underlying optical properties of the volume are unknown, leading to the use of a "best" estimate approach often compromising quantitative accuracy.

AIM

An optimization algorithm is presented that localizes the spatial distribution of bioluminescence by simultaneously recovering the optical properties and location of bioluminescence source from the same set of surface measurements.

APPROACH

Measured data, using implanted self-illuminating sources as well as an orthotopic glioblastoma mouse model, are employed to recover three-dimensional spatial distribution of the bioluminescence source using a multi-parameter optimization algorithm.

RESULTS

The proposed algorithm is able to recover the size and location of the bioluminescence source while accounting for tissue attenuation. Localization accuracies of <1  mm are obtained in all cases, which is similar if not better than current "gold standard" methods that predict optical properties using a different imaging modality.

CONCLUSIONS

Application of this approach, using in-vivo experimental data has shown that quantitative BLT is possible without the need for any prior knowledge about optical parameters, paving the way toward quantitative molecular imaging of exogenous and indigenous biological tumor functionality.

Prior Compensation Algorithm for Cerenkov Luminescence Tomography From Single-View Measurements

Cerenkov luminescence tomography (CLT) has attracted much attention because of the wide clinically-used probes and three-dimensional (3D) quantification ability. However, due to the serious morbidity of 3D optical imaging, the reconstructed images of CLT are not appreciable, especially when single-view measurements are used. Single-view CLT improves the efficiency of data acquisition. It is much consistent with the actual imaging environment of using commercial imaging system, but bringing the problem that the reconstructed results will be closer to the animal surface on the side where the single-view image is collected. To avoid this problem to the greatest extent possible, we proposed a prior compensation algorithm for CLT reconstruction based on depth calibration strategy. This method takes full account of the fact that the attenuation of light in the tissue will depend heavily on the depth of the light source as well as the distance between the light source and the detection plane. Based on this consideration, a depth calibration matrix was designed to calibrate the attenuation between the surface light flux and the density of the internal light source. The feature of the algorithm was that the depth calibration matrix directly acts on the system matrix of CLT reconstruction, rather than modifying the regularization penalty items. The validity and effectiveness of the proposed algorithm were evaluated with a numerical simulation and a mouse-based experiment, whose results illustrated that it located the radiation sources accurately by using single-view measurements.

Simultaneous diffuse optical and bioluminescence tomography to account for signal attenuation to improve source localization

Photonics based pre-clinical imaging is an extensively used technique to allow for the study of biologically relevant activity typically within a small-mouse model. Namely, bioluminescent tomography (BLT) attempts to tomographically reconstruct the 3-dimensional spatial light distribution of luminophores within a small animal given surface light measurements and known underlying optical parameters. Often it is the case where these optical parameters are unknown leading to the use of a 'best' guess approach or to direct measurements using either a multi-modal or dedicated system. Using these conventional approaches can lead to both inaccurate results and extending periods of imaging time. This work introduces the development of an algorithm that is used to accurately localize the spatial light distribution from a bioluminescence source within a subject by simultaneously reconstructing both the underlying optical properties and source spatial distribution and intensity from the same set of surface measurements. Through its application in 2- and 3-dimensional, homogeneous and heterogenous numerical models, it is demonstrated that the proposed algorithm is capable of replicating results as compared to 'gold' standard where the absolute optical properties are known. Additionally, the algorithm has been applied to experimental data using a tissue mimicking block phantom, recovering a spatial light distribution that has a localization error of ∼1.53 mm, which is better than previously published results without the need of assumptions regarding the underlying optical properties or source distribution.

Single pixel hyperspectral bioluminescence tomography based on compressive sensing

Photonics based imaging is a widely utilised technique for the study of biological functions within pre-clinical studies. Specifically, bioluminescence imaging is a sensitive non-invasive and non-contact optical imaging technique that is able to detect distributed (biologically informative) visible and near-infrared activated light sources within tissue, providing information about tissue function. Compressive sensing (CS) is a method of signal processing that works on the basis that a signal or image can be compressed without important information being lost. This work describes the development of a CS based hyperspectral Bioluminescence imaging system that is used to collect compressed fluence data from the external surface of an animal model, due to an internal source, providing lower acquisition times, higher spectral content and potentially better tomographic source localisation. The work demonstrates that hyperspectral surface fluence images of both block and mouse shaped phantom due to internal light sources could be obtained at 30% of the time and measurements it would take to collect the data using conventional raster scanning methods. Using hyperspectral data, tomographic reconstruction of internal light sources can be carried out using any desired number of wavelengths and spectral bandwidth. Reconstructed images of internal light sources using four wavelengths as obtained through CS are presented showing a localisation error of ∼3 mm. Additionally, tomographic images of dual-colored sources demonstrating multi-wavelength light sources being recovered are presented further highlighting the benefits of the hyperspectral system for utilising multi-colored biomarker applications.

Quantitative bioluminescence tomography using spectral derivative data

Bioluminescence imaging (BLI) is a non-contact, optical imaging technique based on measurement of emitted light due to an internal source, which is then often directly related to cellular activity. It is widely used in pre-clinical small animal imaging studies to assess the progression of diseases such as cancer, aiding in the development of new treatments and therapies. For many applications, the quantitative assessment of accurate cellular activity and spatial distribution is desirable as it would enable direct monitoring for prognostic evaluation. This requires quantitative spatially-resolved measurements of bioluminescence source strength inside the animal to be obtained from BLI images. This is the goal of bioluminescence tomography (BLT) in which a model of light propagation through tissue is combined with an optimization algorithm to reconstruct a map of the underlying source distribution. As most models consider only the propagation of light from internal sources to the animal skin surface, an additional challenge is accounting for the light propagation from the skin to the optical detector (e.g. camera). Existing approaches typically use a model of the imaging system optics (e.g. ray-tracing, analytical optical models) or approximate corrections derived from calibration measurements. However, these approaches are typically computationally intensive or of limited accuracy. In this work, a new approach is presented in which, rather than directly using BLI images acquired at several wavelengths, the spectral derivative of that data (difference of BLI images at adjacent wavelengths) is used in BLT. As light at similar wavelengths encounters a near-identical system response (path through the optics etc.) this eliminates the need for additional corrections or system models. This approach is applied to BLT with simulated and experimental phantom data and shown that the error in reconstructed source intensity is reduced from 49% to 4%. Qualitatively, the accuracy of source localization is improved in both simulated and experimental data, as compared to reconstruction using the standard approach. The outlined algorithm can widely be adapted to all commercial systems without any further technological modifications.

Ultrasound-mediation of self-illuminating reporters improves imaging resolution in optically scattering media

In vivo imaging of self-illuminating bio-and chemiluminescent reporters is used to observe the physiology of small animals. However, strong light scattering by biological tissues results in poor spatial resolution of the optical imaging, which also degrades the quantitative accuracy. To overcome this challenging problem, focused ultrasound is used to modulate the light from the reporter at the ultrasound frequency. This produces an ultrasound switchable light 'beacon' that reduces the influence of light scattering in order to improve spatial resolution. The experimental results demonstrate that apart from light modulation at the ultrasound frequency (AC signal at 3.5 MHz), ultrasound also increases the DC intensity of the reporters. This is shown to be due to a temperature rise caused by insonification that was minimized to be within acceptable mammalian tissue safety thresholds by adjusting the duty cycle of the ultrasound. Line scans of bio-and chemiluminescent objects embedded within a scattering medium were obtained using ultrasound modulated (AC) and ultrasound enhanced (DC) signals. Lateral resolution is improved by a factor of 12 and 7 respectively, as compared to conventional CCD imaging. Two chemiluminescent sources separated by ~10 mm at ~20 mm deep inside a 50 mm thick chicken breast have been successfully resolved with an average signal-to-noise ratio of approximately 8-10 dB.

Bayesian sparse-based reconstruction in bioluminescence tomography improves localization accuracy and reduces computational time

Bioluminescence tomography (BLT) provides fundamental insight into biological processes in vivo. To fully realize its potential, it is important to develop image reconstruction algorithms that accurately visualize and quantify the bioluminescence signals taking advantage of limited boundary measurements. In this study, a new 2-step reconstruction method for BLT is developed by taking advantage of the sparse a priori information of the light emission using multispectral measurements. The first step infers a wavelength-dependent prior by using all multi-wavelength measurements. The second step reconstructs the source distribution based on this developed prior. Simulation, phantom and in vivo results were performed to assess and compare the accuracy and the computational efficiency of this algorithm with conventional sparsity-promoting BLT reconstruction algorithms, and results indicate that the position errors are reduced from a few millimeters down to submillimeter, and reconstruction time is reduced by 3 orders of magnitude in most cases, to just under a few seconds. The recovery of single objects and multiple (2 and 3) small objects is simulated, and the recovery of images of a mouse phantom and an experimental animal with an existing luminescent source in the abdomen is demonstrated. Matlab code is available at https://github.com/jinchaofeng/code/tree/master.

ESTRO ACROP: Technology for precision small animal radiotherapy research: Optimal use and challenges

Many radiotherapy research centers have recently installed novel research platforms enabling the investigation of the radiation response of tumors and normal tissues in small animal models, possibly in combination with other treatment modalities. Many more research institutes are expected to follow in the coming years. These novel platforms are capable of mimicking human radiotherapy more closely than older technology. To facilitate the optimal use of these novel integrated precision irradiators and various small animal imaging devices, and to maximize the impact of the associated research, the ESTRO committee on coordinating guidelines ACROP (Advisory Committee in Radiation Oncology Practice) has commissioned a report to review the state of the art of the technology used in this new field of research, and to issue recommendations. This report discusses the combination of precision irradiation systems, small animal imaging (CT, MRI, PET, SPECT, bioluminescence) systems, image registration, treatment planning, and data processing. It also provides guidelines for reporting on studies.

Incorporation of an ultrasound and model guided permissible region improves quantitative source recovery in bioluminescence tomography

Bioluminescence imaging has shown great potential for studying and monitoring disease progression in small animal pre-clinical imaging. However, absolute bioluminescence source recovery through tomographic multi-wavelength measurements is often hindered through the lack of quantitative accuracy and suffers from both poor localisation and quantitative recovery. In this work a method to incorporate a permissible region strategy through not only a priori location (permissible region) but also based on a model of light propagation and hence light sensitivity is developed and tested using both simulations and experimental data. Reconstructions on two different numerical models (a simple slab, and the digital version of a heterogeneous mouse) show an improvement of localisation and recovery of intensity (around 25% for the slab model and around 10% for the digital mouse model). This strategy is also used with experimental data from a phantom gel, which demonstrated an improved recovered tomographic image.

Reconstruction Method for In Vivo Bioluminescence Tomography Based on the Split Bregman Iterative and Surrogate Functions

PURPOSE

Bioluminescence tomography (BLT) can provide in vivo three-dimensional (3D) images for quantitative analysis of biological processes in preclinical small animal studies, which is superior than the conventional planar bioluminescence imaging. However, to reconstruct light sources under the skin in 3D with desirable accuracy and efficiency, BLT has to face the ill-posed and ill-conditioned inverse problem. In this paper, we developed a new method for BLT reconstruction, which utilized the mathematical strategies of the split Bregman iterative and surrogate functions (SBISF) method.

PROCEDURES

The proposed method considered the sparsity characteristic of the reconstructed sources. Thus, the sparsity itself was regarded as a kind of a priori information, and the sparse regularization is incorporated, which can accurately locate the position of the sources. Numerical simulation experiments of multisource cases with comparative analyses were performed to evaluate the performance of the proposed method. Then, a bead-implanted mouse and a breast cancer xenograft mouse model were employed to validate the feasibility of this method in in vivo experiments.

RESULTS

The results of both simulation and in vivo experiments indicated that comparing with the L1-norm iteration shrinkage method and non-monotone spectral projected gradient pursuit method, the proposed SBISF method provided the smallest position error with the least amount of time consumption.

CONCLUSIONS

The SBISF method is able to achieve high accuracy and high efficiency in BLT reconstruction and hold great potential for making BLT more practical in small animal studies.

Development of computational small animal models and their applications in preclinical imaging and therapy research

The development of multimodality preclinical imaging techniques and the rapid growth of realistic computer simulation tools have promoted the construction and application of computational laboratory animal models in preclinical research. Since the early 1990s, over 120 realistic computational animal models have been reported in the literature and used as surrogates to characterize the anatomy of actual animals for the simulation of preclinical studies involving the use of bioluminescence tomography, fluorescence molecular tomography, positron emission tomography, single-photon emission computed tomography, microcomputed tomography, magnetic resonance imaging, and optical imaging. Other applications include electromagnetic field simulation, ionizing and nonionizing radiation dosimetry, and the development and evaluation of new methodologies for multimodality image coregistration, segmentation, and reconstruction of small animal images. This paper provides a comprehensive review of the history and fundamental technologies used for the development of computational small animal models with a particular focus on their application in preclinical imaging as well as nonionizing and ionizing radiation dosimetry calculations. An overview of the overall process involved in the design of these models, including the fundamental elements used for the construction of different types of computational models, the identification of original anatomical data, the simulation tools used for solving various computational problems, and the applications of computational animal models in preclinical research. The authors also analyze the characteristics of categories of computational models (stylized, voxel-based, and boundary representation) and discuss the technical challenges faced at the present time as well as research needs in the future.

Bioluminescence Tomography-Guided Radiation Therapy for Preclinical Research

PURPOSE

In preclinical radiation research, it is challenging to localize soft tissue targets based on cone beam computed tomography (CBCT) guidance. As a more effective method to localize soft tissue targets, we developed an online bioluminescence tomography (BLT) system for small-animal radiation research platform (SARRP). We demonstrated BLT-guided radiation therapy and validated targeting accuracy based on a newly developed reconstruction algorithm.

METHODS AND MATERIALS

The BLT system was designed to dock with the SARRP for image acquisition and to be detached before radiation delivery. A 3-mirror system was devised to reflect the bioluminescence emitted from the subject to a stationary charge-coupled device (CCD) camera. Multispectral BLT and the incomplete variables truncated conjugate gradient method with a permissible region shrinking strategy were used as the optimization scheme to reconstruct bioluminescent source distributions. To validate BLT targeting accuracy, a small cylindrical light source with high CBCT contrast was placed in a phantom and also in the abdomen of a mouse carcass. The center of mass (CoM) of the source was recovered from BLT and used to guide radiation delivery. The accuracy of the BLT-guided targeting was validated with films and compared with the CBCT-guided delivery. In vivo experiments were conducted to demonstrate BLT localization capability for various source geometries.

RESULTS

Online BLT was able to recover the CoM of the embedded light source with an average accuracy of 1 mm compared to that with CBCT localization. Differences between BLT- and CBCT-guided irradiation shown on the films were consistent with the source localization revealed in the BLT and CBCT images. In vivo results demonstrated that our BLT system could potentially be applied for multiple targets and tumors.

CONCLUSIONS

The online BLT/CBCT/SARRP system provides an effective solution for soft tissue targeting, particularly for small, nonpalpable, or orthotopic tumor models.

Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography

Bioluminescence imaging is a noninvasive technique whereby surface weighted images of luminescent probes within animals are used to characterize cell count and function. Traditionally, data are collected over the entire emission spectrum of the source using no filters and are used to evaluate cell count/function over the entire spectrum. Alternatively, multispectral data over several wavelengths can be incorporated to perform tomographic reconstruction of source location and intensity. However, bandpass filters used for multispectral data acquisition have a specific bandwidth, which is ignored in the reconstruction. In this work, ignoring the bandwidth is shown to introduce a dependence of the recovered source intensity on the bandwidth of the filters. A method of accounting for the bandwidth of filters used during multispectral data acquisition is presented and its efficacy in increasing the quantitative accuracy of bioluminescence tomography is demonstrated through simulation and experiment. It is demonstrated that while using filters with a large bandwidth can dramatically decrease the data acquisition time, if not accounted for, errors of up to 200% in quantitative accuracy are introduced in two-dimensional planar imaging, even after normalization. For tomographic imaging, the use of this method to account for filter bandwidth dramatically improves the quantitative accuracy.

Reconstruction Method for Optical Tomography Based on the Linearized Bregman Iteration with Sparse Regularization

Optical molecular imaging is a promising technique and has been widely used in physiology, and pathology at cellular and molecular levels, which includes different modalities such as bioluminescence tomography, fluorescence molecular tomography and Cerenkov luminescence tomography. The inverse problem is ill-posed for the above modalities, which cause a nonunique solution. In this paper, we propose an effective reconstruction method based on the linearized Bregman iterative algorithm with sparse regularization (LBSR) for reconstruction. Considering the sparsity characteristics of the reconstructed sources, the sparsity can be regarded as a kind of a priori information and sparse regularization is incorporated, which can accurately locate the position of the source. The linearized Bregman iteration method is exploited to minimize the sparse regularization problem so as to further achieve fast and accurate reconstruction results. Experimental results in a numerical simulation and in vivo mouse demonstrate the effectiveness and potential of the proposed method.

Analytical reconstruction of the bioluminescent source with priors

Bioluminescence imaging has been a popular tool in small animal imaging. During the last decade, the efforts have focused on the development of tomographic systems. However, due to the difficulties in the nature of inverse source problem, multi-modal systems have been the center of attention for the last couple of years. These systems provide complementary information such that the difficulties of the inverse source problem could be overcome using the a priori information obtained. Motivated by these advances in multi-modal systems, this work presents a novel analytical reconstruction of the bioluminescent source. It is shown that if source strength is known a priori then source position could be calculated or vice versa, if source location is known a priori, source strength could be calculated as well as the photon fluence rate. The determination of the source location can be achieved by another imaging system such as X-ray computed tomography. Therefore, in bioluminescence tomography together with an imaging system can be utilized as a multi-modal system. In this work, conventional finite element based simulations are also performed and the numerical results are compared with the analytical ones. It turns out to be that the analytical results are in a good accordance with the numerical results.

Ultrasound-modulated bioluminescence tomography

We propose a method to reconstruct the density of a luminescent source in a highly scattering medium from ultrasound-modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the diffusion equation.

Quantitative surface radiance mapping using multiview images of light-emitting turbid media

A novel method is presented for accurately reconstructing a spatially resolved map of diffuse light flux on a surface using images of the surface and a model of the imaging system. This is achieved by applying a model-based reconstruction algorithm with an existing forward model of light propagation through free space that accounts for the effects of perspective, focus, and imaging geometry. It is shown that flux can be mapped reliably and quantitatively accurately with very low error, <3% with modest signal-to-noise ratio. Simulation shows that the method is generalizable to the case in which mirrors are used in the system and therefore multiple views can be combined in reconstruction. Validation experiments show that physical diffuse phantom surface fluxes can also be reconstructed accurately with variability <3% for a range of object positions, variable states of focus, and different orientations. The method provides a new way of making quantitatively accurate noncontact measurements of the amount of light leaving a diffusive medium, such as a small animal containing fluorescent or bioluminescent markers, that is independent of the imaging system configuration and surface position.

A Multi-Camera System for Bioluminescence Tomography in Preclinical Oncology Research

Bioluminescent imaging (BLI) of cells expressing luciferase is a valuable noninvasive technique for investigating molecular events and tumor dynamics in the living animal. Current usage is often limited to planar imaging, but tomographic imaging can enhance the usefulness of this technique in quantitative biomedical studies by allowing accurate determination of tumor size and attribution of the emitted light to a specific organ or tissue. Bioluminescence tomography based on a single camera with source rotation or mirrors to provide additional views has previously been reported. We report here in vivo studies using a novel approach with multiple rotating cameras that, when combined with image reconstruction software, provides the desired representation of point source metastases and other small lesions. Comparison with MRI validated the ability to detect lung tumor colonization in mouse lung.

A generalized hybrid algorithm for bioluminescence tomography

Bioluminescence tomography (BLT) is a promising optical molecular imaging technique on the frontier of biomedical optics. In this paper, a generalized hybrid algorithm has been proposed based on the graph cuts algorithm and gradient-based algorithms. The graph cuts algorithm is adopted to estimate a reliable source support without prior knowledge, and different gradient-based algorithms are sequentially used to acquire an accurate and fine source distribution according to the reconstruction status. Furthermore, multilevel meshes for the internal sources are used to speed up the computation and improve the accuracy of reconstruction. Numerical simulations have been performed to validate this proposed algorithm and demonstrate its high performance in the multi-source situation even if the detection noises, optical property errors and phantom structure errors are involved in the forward imaging.

Hybrid multilevel sparse reconstruction for a whole domain bioluminescence tomography using adaptive finite element

Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed with in vivo experiments.

Multi-modal molecular diffuse optical tomography system for small animal imaging

A multi-modal optical imaging system for quantitative 3D bioluminescence and functional diffuse imaging is presented, which has no moving parts and uses mirrors to provide multi-view tomographic data for image reconstruction. It is demonstrated that through the use of trans-illuminated spectral near infrared measurements and spectrally constrained tomographic reconstruction, recovered concentrations of absorbing agents can be used as prior knowledge for bioluminescence imaging within the visible spectrum. Additionally, the first use of a recently developed multi-view optical surface capture technique is shown and its application to model-based image reconstruction and free-space light modelling is demonstrated. The benefits of model-based tomographic image recovery as compared to 2D planar imaging are highlighted in a number of scenarios where the internal luminescence source is not visible or is confounding in 2D images. The results presented show that the luminescence tomographic imaging method produces 3D reconstructions of individual light sources within a mouse-sized solid phantom that are accurately localised to within 1.5mm for a range of target locations and depths indicating sensitivity and accurate imaging throughout the phantom volume. Additionally the total reconstructed luminescence source intensity is consistent to within 15% which is a dramatic improvement upon standard bioluminescence imaging. Finally, results from a heterogeneous phantom with an absorbing anomaly are presented demonstrating the use and benefits of a multi-view, spectrally constrained coupled imaging system that provides accurate 3D luminescence images.

Comparative studies of l(p)-regularization-based reconstruction algorithms for bioluminescence tomography

Inverse source reconstruction is the most challenging aspect of bioluminescence tomography (BLT) because of its ill-posedness. Although many efforts have been devoted to this problem, so far, there is no generally accepted method. Due to the ill-posedness property of the BLT inverse problem, the regularization method plays an important role in the inverse reconstruction. In this paper, six reconstruction algorithms based on l(p) regularization are surveyed. The effects of the permissible source region, measurement noise, optical properties, tissue specificity and source locations on the performance of the reconstruction algorithms are investigated using a series of single source experiments. In order to further inspect the performance of the reconstruction algorithms, we present the double sources and the in vivo mouse experiments to study their resolution ability and potential for a practical heterogeneous mouse experiment. It is hoped to provide useful guidance on algorithm development and application in the related fields.

Sparse reconstruction for bioluminescence tomography based on the semigreedy method

Bioluminescence tomography (BLT) is a molecular imaging modality which can three-dimensionally resolve the molecular processes in small animals in vivo. The ill-posedness nature of BLT problem makes its reconstruction bears nonunique solution and is sensitive to noise. In this paper, we proposed a sparse BLT reconstruction algorithm based on semigreedy method. To reduce the ill-posedness and computational cost, the optimal permissible source region was automatically chosen by using an iterative search tree. The proposed method obtained fast and stable source reconstruction from the whole body and imposed constraint without using a regularization penalty term. Numerical simulations on a mouse atlas, and in vivo mouse experiments were conducted to validate the effectiveness and potential of the method.

Efficient sparse reconstruction algorithm for bioluminescence tomography based on duality and variable splitting

Bioluminescence tomography (BLT) can three-dimensionally and quantitatively resolve the molecular processes in small animals in vivo. In this paper, we propose a BLT reconstruction algorithm based on duality and variable splitting. By using duality and variable splitting to obtain a new equivalent constrained optimization problem and updating the primal variable as the Lagrangian multiplier in the dual augmented Lagrangian problem, the proposed method can obtain fast and stable source reconstruction even without the permissible source region and multispectral measurements. Numerical simulations on a mouse atlas and in vivo mouse experiments were conducted to validate the effectiveness and potential of the method.

Total variation regularization for bioluminescence tomography with the split Bregman method

Regularization methods have been broadly applied to bioluminescence tomography (BLT) to obtain stable solutions, including l2 and l1 regularizations. However, l2 regularization can oversmooth reconstructed images and l1 regularization may sparsify the source distribution, which degrades image quality. In this paper, the use of total variation (TV) regularization in BLT is investigated. Since a nonnegativity constraint can lead to improved image quality, the nonnegative constraint should be considered in BLT. However, TV regularization with a nonnegativity constraint is extremely difficult to solve due to its nondifferentiability and nonlinearity. The aim of this work is to validate the split Bregman method to minimize the TV regularization problem with a nonnegativity constraint for BLT. The performance of split Bregman-resolved TV (SBRTV) based BLT reconstruction algorithm was verified with numerical and in vivo experiments. Experimental results demonstrate that the SBRTV regularization can provide better regularization quality over l2 and l1 regularizations.

An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography

PURPOSE

Bioluminescence tomography (BLT) provides an effective tool for monitoring physiological and pathological activities in vivo. However, the measured data in bioluminescence imaging are corrupted by noise. Therefore, regularization methods are commonly used to find a regularized solution. Nevertheless, for the quality of the reconstructed bioluminescent source obtained by regularization methods, the choice of the regularization parameters is crucial. To date, the selection of regularization parameters remains challenging. With regards to the above problems, the authors proposed a BLT reconstruction algorithm with an adaptive parameter choice rule.

METHODS

The proposed reconstruction algorithm uses a diffusion equation for modeling the bioluminescent photon transport. The diffusion equation is solved with a finite element method. Computed tomography (CT) images provide anatomical information regarding the geometry of the small animal and its internal organs. To reduce the ill-posedness of BLT, spectral information and the optimal permissible source region are employed. Then, the relationship between the unknown source distribution and multiview and multispectral boundary measurements is established based on the finite element method and the optimal permissible source region. Since the measured data are noisy, the BLT reconstruction is formulated as l(2) data fidelity and a general regularization term. When choosing the regularization parameters for BLT, an efficient model function approach is proposed, which does not require knowledge of the noise level. This approach only requests the computation of the residual and regularized solution norm. With this knowledge, we construct the model function to approximate the objective function, and the regularization parameter is updated iteratively.

RESULTS

First, the micro-CT based mouse phantom was used for simulation verification. Simulation experiments were used to illustrate why multispectral data were used rather than monochromatic data. Furthermore, the study conducted using an adaptive regularization parameter demonstrated our ability to accurately localize the bioluminescent source. With the adaptively estimated regularization parameter, the reconstructed center position of the source was (20.37, 31.05, 12.95) mm, and the distance to the real source was 0.63 mm. The results of the dual-source experiments further showed that our algorithm could localize the bioluminescent sources accurately. The authors then presented experimental evidence that the proposed algorithm exhibited its calculated efficiency over the heuristic method. The effectiveness of the new algorithm was also confirmed by comparing it with the L-curve method. Furthermore, various initial speculations regarding the regularization parameter were used to illustrate the convergence of our algorithm. Finally, in vivo mouse experiment further illustrates the effectiveness of the proposed algorithm.

CONCLUSIONS

Utilizing numerical, physical phantom and in vivo examples, we demonstrated that the bioluminescent sources could be reconstructed accurately with automatic regularization parameters. The proposed algorithm exhibited superior performance than both the heuristic regularization parameter choice method and L-curve method based on the computational speed and localization error.

Multimodal image coregistration and inducible selective cell ablation to evaluate imaging ligands

We combined multimodal imaging (bioluminescence, X-ray computed tomography, and PET), tomographic reconstruction of bioluminescent sources, and two unique, complementary models to evaluate three previously synthesized PET radiotracers thought to target pancreatic beta cells. The three radiotracers {[(18)F]fluoropropyl-(+)-dihydrotetrabenazine ([(18)F]FP-DTBZ), [(18)F](+)-2-oxiranyl-3-isobutyl-9-(3-fluoropropoxy)-10-methoxy-2,3,4,6,7,11b-hexahydro-1H-pyrido[2,1-a]isoquinoline ((18)F-AV-266), and (2S,3R,11bR)-9-(3-fluoropropoxy)-2-(hydroxymethyl)-3-isobutyl-10-methoxy-2,3,4,6,7,11b-hexahydro-1H-pyrido[2,1-a]isoquinolin-2-ol ((18)F-AV-300)} bind vesicular monoamine transporter 2. Tomographic reconstruction of the bioluminescent signal in mice expressing luciferase only in pancreatic beta cells was used to delineate the pancreas and was coregistered with PET and X-ray computed tomography images. This strategy enabled unambiguous identification of the pancreas on PET images, permitting accurate quantification of the pancreatic PET signal. We show here that, after conditional, specific, and rapid mouse beta-cell ablation, beta-cell loss was detected by bioluminescence imaging but not by PET imaging, given that the pancreatic signal provided by three PET radiotracers was not altered. To determine whether these ligands bound human beta cells in vivo, we imaged mice transplanted with luciferase-expressing human islets. The human islets were imaged by bioluminescence but not with the PET ligands, indicating that these vesicular monoamine transporter 2-directed ligands did not specifically bind beta cells. These data demonstrate the utility of coregistered multimodal imaging as a platform for evaluation and validation of candidate ligands for imaging islets.

Implicit and explicit prior information in near-infrared spectral imaging: accuracy, quantification and diagnostic value

Near-infrared spectroscopy (NIRS) of tissue provides quantification of absorbers, scattering and luminescent agents in bulk tissue through the use of measurement data and assumptions. Prior knowledge can be critical about things such as (i) the tissue shape and/or structure, (ii) spectral constituents, (iii) limits on parameters, (iv) demographic or biomarker data, and (v) biophysical models of the temporal signal shapes. A general framework of NIRS imaging with prior information is presented, showing that prior information datasets could be incorporated at any step in the NIRS process, with the general workflow being: (i) data acquisition, (ii) pre-processing, (iii) forward model, (iv) inversion/reconstruction, (v) post-processing, and (vi) interpretation/diagnosis. Most of the development in NIRS has used ad hoc or empirical implementations of prior information such as pre-measured absorber or fluorophore spectra, or tissue shapes as estimated by additional imaging tools. A comprehensive analysis would examine what prior information maximizes the accuracy in recovery and value for medical diagnosis, when implemented at separate stages of the NIRS sequence. Individual applications of prior information can show increases in accuracy or improved ability to estimate biochemical features of tissue, while other approaches may not. Most beneficial inclusion of prior information has been in the inversion/reconstruction process, because it solves the mathematical intractability. However, it is not clear that this is always the most beneficial stage.

Comparison of permissible source region and multispectral data using efficient bioluminescence tomography method

As a novel molecular imaging technology, bioluminescence tomography (BLT) has become an important tool for biomedical research in recent years, which can perform a quantitative reconstruction of an internal light source distribution with the scattered and transmitted bioluminescent signals measured on the external surface of a small animal. However, BLT is severely ill-posed because of complex photon propagation in the biological tissue and limited boundary measured data with noise. Therefore, sufficient a priori knowledge should be fused for the uniqueness and stability of BLT solution. Permissible source region strategy and spectrally resolved measurements are two kinds of a priori knowledge commonly used in BLT reconstruction. This paper compares their performance with simulation and in vivo heterogeneous mouse experiments. In order to improve the efficiency of large-scale source restoration, this paper introduces an efficient iterative shrinkage thresholding method that not only has faster convergence rate but also has better reconstruction accuracy than the modified Newton-type optimization approach. Finally, a discussion of these two kinds of a priori knowledge is given based on the comparison results.

Total variation regularization for bioluminescence tomography with an adaptive parameter choice approach

In this paper, we explore the application of total variation regularization method for bioluminescence tomography (BLT) with an adaptive regularization parameter choice approach. Since BLT is a seriously ill-posed problem, therefore, l(2) regularized methods are frequently adopted to recover the bi-oluminescent sources. However, l(2) regularized methods typically lead to smooth reconstructions. In this paper, we investigated the use of total variation (TV) regularization to improve the quality of BLT reconstruction. Furthermore, the regularization parameter in TV method was chosen adaptively to make the proposed algorithm more stable. Results on simulation data provide evidence that the reconstructed source can be localized accurately compared with l(2) method. Meanwhile, the effectiveness of utility of the parameter choice were illustrated. Finally, different levels of noisy data were added to validate the performance of the proposed algorithm.

An optical-parameters-free method for locating light source in deep tissue

Bioluminescence of luciferase-expressing cells in live animals is a promising technique for image guided tumor resection. However, requiring exact optical tissue parameters is an underlying problem of diffusion equation when recovering bioluminescent images of luciferase activity within a volume using emission optical signal data from internal light sources. In this paper, an equivalence method based on the equation of radiative transfer (ERT) is proposed to locate bioluminescence source without optical tissue parameters. The solution of equivalence method is satisfied with the unique of localization as well as the complex tissue environment. The reconstructed images of bioluminescence are presented with simulated heterogeneous tissue models, and an 8.7% relative error of the source localization is obtained.

Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.

Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method

Bioluminescence tomography (BLT) is a promising tool for studying physiological and pathological processes at cellular and molecular levels. In most clinical or preclinical practices, fine discretization is needed for recovering sources with acceptable resolution when solving BLT with finite element method (FEM). Nevertheless, uniformly fine meshes would cause large dataset and overfine meshes might aggravate the ill-posedness of BLT. Additionally, accurately quantitative information of density and power has not been simultaneously obtained so far. In this paper, we present a novel multilevel sparse reconstruction method based on adaptive FEM framework. In this method, permissible source region gradually reduces with adaptive local mesh refinement. By using sparse reconstruction with l(1) regularization on multilevel adaptive meshes, simultaneous recovery of density and power as well as accurate source location can be achieved. Experimental results for heterogeneous phantom and mouse atlas model demonstrate its effectiveness and potentiality in the application of quantitative BLT.

3D reconstruction of light flux distribution on arbitrary surfaces from 2D multi-photographic images

Optical tomography can demonstrate accurate three-dimensional (3D) imaging that recovers the 3D spatial distribution and concentration of the luminescent probes in biological tissues, compared with planar imaging. However, the tomographic approach is extremely difficult to implement due to the complexity in the reconstruction of 3D surface flux distribution from multi-view two dimensional (2D) measurements on the subject surface. To handle this problem, a novel and effective method is proposed in this paper to determine the surface flux distribution from multi-view 2D photographic images acquired by a set of non-contact detectors. The method is validated with comparison experiments involving both regular and irregular surfaces. Reconstruction of the inside probes based on the reconstructed surface flux distribution further demonstrates the potential of the proposed method in its application in optical tomography.

Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem

In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the reconstruction results. Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated. In this paper, the truncated total least squares method (TTLS) is introduced into BLT reconstruction, in which both system errors and measurement noise are taken into account. Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS. Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.

A trust region method in adaptive finite element framework for bioluminescence tomography

Bioluminescence tomography (BLT) is an effective molecular imaging (MI) modality. Because of the ill-posedness, the inverse problem of BLT is still open. We present a trust region method (TRM) for BLT source reconstruction. The TRM is applied in the source reconstruction procedure of BLT for the first time. The results of both numerical simulations and the experiments of cube phantom and nude mouse draw us to the conclusion that based on the adaptive finite element (AFE) framework, the TRM works in the source reconstruction procedure of BLT. To make our conclusion more reliable, we also compare the performance of the TRM and that of the famous Tikhonov regularization method after only one step of mesh refinement of the AFE framework. The conclusion is that the TRM can get faster and better results after only one mesh refinement step of AFE framework than the Tikhonov regularization method when handling large scale data. In the TRM, all the parameters are fixed, while in the Tikhonov method the regularization parameter needs to be well selected.

In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration

PURPOSE

Bioluminescence imaging is a research tool for studying gene expression levels in small animal models of human disease. Bioluminescence light, however, is strongly scattered in biological tissue and no direct image of the light-emitting reporter probe's location can be obtained. Therefore, the authors have developed a linear image reconstruction method for bioluminescence tomography (BLT) that recovers the three-dimensional spatial bioluminescent source distribution in small animals.

METHODS

The proposed reconstruction method uses third-order simplified spherical harmonics (SP3) solutions to the equation of radiative transfer for modeling the bioluminescence light propagation in optically nonuniform tissue. The SP3 equations and boundary conditions are solved with a finite-difference (FD) technique on a regular grid. The curved geometry of the animal surface was taken into account with a blocking-off region method for regular grids. Coregistered computed tomography (CT) and magnetic resonance (MR) images provide information regarding the geometry of the skin surface and internal organs. The inverse source problem is defined as an algebraic system of linear equations for the unknown source distribution and is iteratively solved given multiview and multispectral boundary measurements. The average tissue absorption parameters, which are used for the image reconstruction process, were calculated with an evolution strategy (ES) from in vivo measurements using an implanted pointlike source of known location and spectrum. Moreover, anatomical information regarding the location of the internal organs and other tissue structures within the animal's body are provided by coregistered MR images.

RESULTS

First, the authors recovered the wavelength-dependent absorption coefficients (average error of 14%) with the ES under ideal conditions by using a numerical mouse model. Next, they reconstructed the average absorption coefficient of a small animal by using an artificial implanted light source and the validated ES. Last, they conducted two in vivo animal experiments and recovered the spatial location of the implanted light source and the spatial distribution of a bioluminescent reporter system located in the kidneys. The source reconstruction results were coregistered to CT and MR images. They further found that accurate bioluminescence image reconstructions could be obtained when segmenting a voidlike cyst with low-scattering and absorption parameters, whereas inaccurate image reconstructions were obtained when assuming a uniform optical parameter distribution instead. The image reconstructions were completed within 23 min on a 3 GHz Intel processor.

CONCLUSIONS

The authors demonstrated on in vivo examples that the combination of anatomical coregistration, accurate optical tissue properties, multispectral acquisition, and a blocking-off FD-SP3 solution of the radiative transfer model significantly improves the accuracy of the BLT reconstructions.

Image reconstruction in diffuse optical tomography based on simplified spherical harmonics approximation

The use of higher order approximations to the Radiative transport equation, through simplified spherical harmonics expansion (SP(N)) in optical tomography are presented. It is shown that, although the anisotropy factor can be modeled in the forward problem, its sensitivity to the measured boundary data is limited to superficial regions and more importantly, due to uniqueness of the inverse problem it cannot be determined using frequency domain data. Image reconstruction through the use of higher ordered models is presented. It is demonstrated that at higher orders (for example SP7) the image reconstruction becomes highly under-determined due to the large increase in the number of unknowns which cannot be adequately recovered. However, reconstruction of diffuse parameters, namely optical absorption and reduced scatter have shown to be more accurate where only the sensitivity matrix used in the inverse problem is based on SP(N) method and image reconstruction is limited to these two diffuse parameters.

Registration of planar bioluminescence to magnetic resonance and x-ray computed tomography images as a platform for the development of bioluminescence tomography reconstruction algorithms

The procedures we propose make possible the mapping of two-dimensional (2-D) bioluminescence image (BLI) data onto a skin surface derived from a three-dimensional (3-D) anatomical modality [magnetic resonance (MR) or computed tomography (CT)] dataset. This mapping allows anatomical information to be incorporated into bioluminescence tomography (BLT) reconstruction procedures and, when applied using sources visible to both optical and anatomical modalities, can be used to evaluate the accuracy of those reconstructions. Our procedures, based on immobilization of the animal and a priori determined fixed projective transforms, should be more robust and accurate than previously described efforts, which rely on a poorly constrained retrospectively determined warping of the 3-D anatomical information. Experiments conducted to measure the accuracy of the proposed registration procedure found it to have a mean error of 0.36+/-0.23 mm. Additional experiments highlight some of the confounds that are often overlooked in the BLT reconstruction process, and for two of these confounds, simple corrections are proposed.