Fluorescence molecular tomography for quantum yield and lifetime.

Fluorescence molecular tomography (FMT) is a promising modality for noninvasive imaging of internal fluorescence agents in biological tissues, especially in small animal models, with applications in diagnosis, therapy, and drug design. In this paper, we present a fluorescent reconstruction algorithm that combines time-resolved fluorescence imaging data with photon-counting microcomputed tomography (PCMCT) images to estimate the quantum yield and lifetime of fluorescent markers in a mouse model. By incorporating PCMCT images, a permissible region of interest of fluorescence yield and lifetime can be roughly estimated as prior knowledge, reducing the number of unknown variables in the inverse problem and improving the image reconstruction stability. Our numerical experiments demonstrate the accuracy and stability of the proposed reconstruction method in the presence of data noise, achieving a reconstruction error of 0.02 ns for the fluorescence lifetime and an average relative error of 18% for quantum yield reconstruction.

Estimating optical parameters of biological tissues with photon-counting micro-CT.

Wavelength-dependent absorption and scattering properties determine the fluorescence photon transport in biological tissues and image resolution of optical molecular tomography. Currently, these parameters are computed from optically measured data. For small animal imaging, estimation of optical parameters is a large-scale optimization problem, which is highly ill-posed. In this paper, we propose a new, to the best of our knowledge, approach to estimate optical parameters of biological tissues with photon-counting micro-computed tomography (micro-CT). From photon-counting x-ray data, multi-energy micro-CT images can be reconstructed to perform multi-organ segmentation and material decomposition in terms of tissue constituents. The concentration and characteristics of major tissue constituents can be utilized to calculate the optical absorption and scattering coefficients of the involved tissues. In our study, we perform numerical simulation, phantom experiments, and in vivo animal studies to calculate the optical parameters using our proposed approach. The results show that our approach can estimate optical parameters of tissues with a relative error of <10%, accurately mapping the optical parameter distributions in a small animal.

Projection decomposition via univariate optimization for dual-energy CT.

Dual-energy computed tomography (DECT) acquires two x-ray projection datasets with different x-ray energy spectra, performs material-specific image reconstruction based on the energy-dependent non-linear integral model, and provides more accurate quantification of attenuation coefficients than single energy spectrum CT. In the diagnostic energy range, x-ray energy-dependent attenuation is mainly caused by photoelectric absorption and Compton scattering. Theoretically, these two physical components of the x-ray attenuation mechanism can be determined from two projection datasets with distinct energy spectra. Practically, the solution of the non-linear integral equation is complicated due to spectral uncertainty, detector sensitivity, and data noise. Conventional multivariable optimization methods are prone to local minima. In this paper, we develop a new method for DECT image reconstruction in the projection domain. This method combines an analytic solution of a polynomial equation and a univariate optimization to solve the polychromatic non-linear integral equation. The polynomial equation of an odd order has a unique real solution with sufficient accuracy for image reconstruction, and the univariate optimization can achieve the global optimal solution, allowing accurate and stable projection decomposition for DECT. Numerical and physical phantom experiments are performed to demonstrate the effectiveness of the method in comparison with the state-of-the-art projection decomposition methods. As a result, the univariate optimization method yields a quality improvement of 15% for image reconstruction and substantial reduction of the computational time, as compared to the multivariable optimization methods.

Clinical validation of CT image reconstruction with interior tomography.

Active x-ray collimation is well adopted in radiography and fluoroscopy for radiation dose reduction and image quality improvement. The application of this concept in computed tomography (CT) is significantly limited due to the truncation of projection data. Generally, an internal field of view (FOV) inside an imaging object cannot be exactly reconstructed only from the truncated projection data. Recent research shows that given some prior information of the FOV image, interior tomography can provide a unique and stable solution for image reconstruction of an internal FOV. The objective of this study is to evaluate the performance of interior reconstruction based on patient datasets obtained from a clinical CT scanner with dual x-ray tubes, which simultaneously gives full projections and truncated projections. Image reconstructions are performed from full and truncated projection data for the comparison of image quality, respectively. The reconstructed CT images were reviewed by a radiologist and a resident. The evaluation results of two observers showed that CT images reconstructed with truncated projections met clinically diagnostic requirements and were comparable to clinical images. This study demonstrates that with the development of interior tomography, active x-ray collimation in the imaging plane can be readily employed in CT imaging to further reduce patient radiation and improve image quality.

Model and reconstruction of a K-edge contrast agent distribution with an X-ray photon-counting detector.

Contrast-enhanced computed tomography (CECT) helps enhance the visibility for tumor imaging. When a high-Z contrast agent interacts with X-rays across its K-edge, X-ray photoelectric absorption would experience a sudden increment, resulting in a significant difference of the X-ray transmission intensity between the left and right energy windows of the K-edge. Using photon-counting detectors, the X-ray intensity data in the left and right windows of the K-edge can be measured simultaneously. The differential information of the two kinds of intensity data reflects the contrast-agent concentration distribution. K-edge differences between various matters allow opportunities for the identification of contrast agents in biomedical applications. In this paper, a general radon transform is established to link the contrast-agent concentration to X-ray intensity measurement data. An iterative algorithm is proposed to reconstruct a contrast-agent distribution and tissue attenuation background simultaneously. Comprehensive numerical simulations are performed to demonstrate the merits of the proposed method over the existing K-edge imaging methods. Our results show that the proposed method accurately quantifies a distribution of a contrast agent, optimizing the contrast-to-noise ratio at a high dose efficiency.

Radiative transfer with delta-Eddington-type phase functions.

The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately. One idea to overcome the difficulty associated with the highly forward-peaked scattering is through the use of a delta-Eddington phase function. This paper is devoted to an RTE framework with a family of delta-Eddington-type phase functions. Significance in biomedical imaging applications of the RTE with delta-Eddington-type phase functions are explained. Mathematical studies of the problems include solution existence, uniqueness, and continuous dependence on the problem data: the inflow boundary value, the source function, the absorption coefficient, and the scattering coefficient. Numerical results are presented to show that employing a delta-Eddington-type phase function with properly chosen parameters provides accurate simulation results for light propagation within highly forward-peaked scattering media.

A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT.

Standard computed tomography (CT) cannot reproduce spectral information of an object. Hardware solutions include dual-energy CT which scans the object twice in different x-ray energy levels, and energy-discriminative detectors which can separate lower and higher energy levels from a single x-ray scan. In this paper, we propose a software solution and give an iterative algorithm that reconstructs an image with spectral information from just one scan with a standard energy-integrating detector. The spectral information obtained can be used to produce color CT images, spectral curves of the attenuation coefficient µ(r, E)at points inside the object, and photoelectric images, which are all valuable imaging tools in cancerous diagnosis. Our software solution requires no change on hardware of a CT machine. With the Shepp-Logan phantom, we have found that although the photoelectric and Compton components were not perfectly reconstructed, their composite effect was very accurately reconstructed as compared to the ground truth and the dual-energy CT counterpart. This means that our proposed method has an intrinsic benefit in beam hardening correction and metal artifact reduction. The algorithm is based on a nonlinear polychromatic acquisition model for x-ray CT. The key technique is a sparse representation of iterations in a framelet system. Convergence of the algorithm is studied. This is believed to be the first application of framelet imaging tools to a nonlinear inverse problem.

Fully 3D geometrical calibration for an X-ray grating-based imaging system.

The Precision of geometric parameters is the key requirement for grating-based phase-contrast CT and attenuation-based CT in cone-beam geometry. By extending our fan-beam geometric calibration work via Locally Linear Embedding (LLE) into the cone-beam case, here we calibrate the geometric parameters of our in-house phase-contrast CT system with attenuation projection data. Numerical and experimental studies show that the LLE-based calibration method is feasible to calibrate 8 parameters of the cone-beam geometry that improves reconstruction quality significantly.

X-ray CT geometrical calibration via locally linear embedding.

For X-ray computed tomography (CT), geometric calibration and rigid patient motion compensation are inter-related issues for optimization of image reconstruction quality. Non-calibrated system geometry and patient movement during a CT scan will result in streak-like, blurring and other artifacts in reconstructed images. In this paper, we propose a locally linear embedding based calibration approach to address this challenge under a rigid 2D object assumption and a more general way than what has been reported before. In this method, projections are linearly represented by up-sampled neighbors via locally linear embedding, and CT system parameters are iteratively estimated from projection data themselves. Numerical and experimental studies show that images reconstructed with calibrated parameters are in excellent agreement with the counterparts reconstructed with the true parameters.

Sinogram-based attenuation correction in PET/CT.

In a typical positron emission tomography/computed tomography (PET/CT) system, the attenuation correction is necessary for PET image reconstruction, which involves a transformation from the CT Hounsfield units (HU) to its linear attenuation coefficient (LAC) at 511 keV. This transformation is usually aided by an empirical bilinear function, followed by the forward projection of the transformed attenuation image. In this paper, we propose a direct method that calculates attenuation factors from CT projections, without using a reconstructed CT image. In this method, the human body is considered as a mixture of three distinct components: air, water and bone. Then, we estimate the proportions of these three components along each x-ray path and restore the attenuation factor at 511 keV with the known water and bone LACs. Our numerical results show that the proposed method produces as accurate estimation as the conventional HU mapping method.

A mixed reality approach for stereo-tomographic quantification of lung nodules.

To reduce the radiation dose and the equipment cost associated with lung CT screening, in this paper we propose a mixed reality based nodule measurement method with an active shutter stereo imaging system. Without involving hundreds of projection views and subsequent image reconstruction, we generated two projections of an iteratively placed ellipsoidal volume in the field of view and merging these synthetic projections with two original CT projections. We then demonstrated the feasibility of measuring the position and size of a nodule by observing whether projections of an ellipsoidal volume and the nodule are overlapped from a human observer's visual perception through the active shutter 3D vision glasses. The average errors of measured nodule parameters are less than 1 mm in the simulated experiment with 8 viewers. Hence, it could measure real nodules accurately in the experiments with physically measured projections.

A spectral interior CT by a framelet-based reconstruction algorithm.

Reducing radiation dose is an important goal in medical computed tomography (CT), for which interior tomography is an effective approach. There have been interior reconstruction algorithms for monochromatic CT, but in reality, X-ray sources are polychromatic. Using a polychromatic acquisition model and motivated by framelet-based image processing algorithms, in this paper, we propose an interior reconstruction algorithm to obtain an image with spectral information assuming only one scan with a current energy-integrating detector. This algorithm is a new nonlinear iterative method by minimizing a special functional under a polychromatic acquisition model for X-ray CT, where the attenuation coefficients are energy-dependent. Experimental results validate that our algorithm can effectively reduce the beam-hardening artifacts and metal artifacts. It also produces color overlays which are useful in tumor identification and quantification.

Talbot interferometry with curved quasi-periodic gratings: towards large field of view X-ray phase-contrast imaging.

X-ray phase-contrast imaging based on grating interferometry has become a common method due to its superior contrast in biological soft tissue imaging. The high sensitivity relies on the high-aspect ratio structures of the planar gratings, which prohibit the large field of view applications with a diverging X-ray source. Curved gratings allow a high X-ray flux for a wider angular range, but the interference fringes are only visible within ~10° range due to the geometrical mismatch with the commonly used flat array detectors. In this paper, we propose a design using a curved quasi-periodic grating for large field of view imaging with a flat detector array. Our scheme is numerically verified in the X-ray regime and experimentally verified in the visible optical regime. The interference fringe pattern is observed over 25°, with less than 10% of decrease in visibility in our experiments.

X-ray micro-modulated luminescence tomography (XMLT).

Imaging depth of optical microscopy has been fundamentally limited to millimeter or sub-millimeter due to strong scattering of light in a biological sample. X-ray microscopy can resolve spatial details of few microns deep inside a sample but contrast resolution is inadequate to depict heterogeneous features at cellular or sub-cellular levels. To enhance and enrich biological contrast at large imaging depth, various nanoparticles are introduced and become essential to basic research and molecular medicine. Nanoparticles can be functionalized as imaging probes, similar to fluorescent and bioluminescent proteins. LiGa(5)O(8):Cr(3+) nanoparticles were recently synthesized to facilitate luminescence energy storage with x-ray pre-excitation and subsequently stimulated luminescence emission by visible/near-infrared (NIR) light. In this paper, we propose an x-ray micro-modulated luminescence tomography (XMLT, or MLT to be more general) approach to quantify a nanophosphor distribution in a thick biological sample with high resolution. Our numerical simulation studies demonstrate the feasibility of the proposed approach.

L(p) regularization for early gate fluorescence molecular tomography.

Time domain fluorescence molecular tomography (TD-FMT) provides a unique dataset for enhanced quantification and spatial resolution. The time-gate dataset can be divided into two temporal groups around the maximum counts gate, which are early gates and late gates. It is well established that early gates allow for improved spatial resolution and late gates are essential for fluorophore unmixing and concentration quantification. However, the inverse problem of FMT is ill-posed and typically underdetermined, which makes image reconstruction highly susceptible to data noise. More specifically, photon counts are inherently very low at early gates due to high absorption and scattering of tissue, resulting in a low signal-to-noise ratio and unstable reconstructions. In this work, an L(p) regularization-based reconstruction algorithm was developed and tested with our wide-field mesh-based Monte Carlo simulation strategy. We compared the early time-gate reconstructions obtained with the different p (p∈{1/16,1/8,1/4,1/3,1/2,1,2}) from a synthetic murine model simulating the fluorophore uptake in the kidneys and preclinical data. The results from a 3D mouse atlas and a mouse experiment show that our L(1/4) regularization methods give the best performance for early time gates reconstructions.

Stored luminescence computed tomography.

Phosphor nanoparticles made of doped semiconductors and pre-excited by x-ray radiation were recently reported for their luminescence emission in the range of 650-770 nm upon near-infrared (NIR) light stimulation. These nanophosphors can be functionalized as optical probes for molecular imaging. In this paper, we present stored luminescence computed tomography to reconstruct a nanophosphor distribution in an object. The propagation of x rays in a biological object allows significantly better localization and deeper penetration. Moreover, the nanophosphors, which are pre-excited with collimated x-ray beams or focused x-ray waves, can be successively stimulated for stored luminescence emissions by variable NIR stimulation patterns. The sequentially detected luminescence signals provide more information of a nanophosphor spatial distribution for more accurate image reconstruction and higher image resolution. A realistic numerical study is performed to demonstrate the feasibility and merits of the proposed approach.

Top-level design and pilot analysis of low-end CT scanners based on linear scanning for developing countries.

The goal is to develop new architectures for computed tomography (CT) which are at an ultra-low-cost for developing countries, especially in rural areas. The proposed general scheme is inspired by the recently developed compressive sensing and interior tomography techniques, where the data acquisition system targets a region of interest (ROI) to acquire limited and truncated data. Similar to linear tomosynthesis, the source and detector are translated in opposite directions but in contrast to conventional tomosynthesis, our proposal is for either ROI reconstruction with one or more localized linear scans or global reconstruction by combining multiple ROI reconstructions. In other words, the popular slip ring is replaced by a translation based setup, and the instrumentation cost is reduced by a relaxation of the imaging speed requirement. The various translational scanning modes are theoretically analyzed, and the scanning parameters are optimized. The numerical simulation results from different numbers of linear scans confirm the feasibility of the proposed scheme, and suggest two preferred low-end systems for horizontal and vertical patient positions respectively. Ultra-low-cost x-ray CT is feasible with our proposed combination of linear scanning, compressive sensing, and interior tomography. The proposed architecture can be tailored into permanent, movable, or reconfigurable systems as desirable. Advanced image registration and spectral imaging features can be included as well.

Tomographic Image Reconstruction Using an Advanced Score Function (ADSF).

Computed tomography (CT) reconstructs volumetric images using X-ray projection data acquired from multiple angles around an object. For low-dose or sparse-view CT scans, the classic image reconstruction algorithms often produce severe noise and artifacts. To address this issue, we develop a novel iterative image reconstruction method based on maximum a posteriori (MAP) estimation. In the MAP framework, the score function, i.e., the gradient of the logarithmic probability density distribution, plays a crucial role as an image prior in the iterative image reconstruction process. By leveraging the Gaussian mixture model, we derive a novel score matching formula to establish an advanced score function (ADSF) through deep learning. Integrating the new ADSF into the image reconstruction process, a new ADSF iterative reconstruction method is developed to improve image reconstruction quality. The convergence of the ADSF iterative reconstruction algorithm is proven through mathematical analysis. The performance of the ADSF reconstruction method is also evaluated on both public medical image datasets and clinical raw CT datasets. Our results show that the ADSF reconstruction method can achieve better denoising and deblurring effects than the state-of-the-art reconstruction methods, showing excellent generalizability and stability.

X-ray fluorescence tomographic system design and image reconstruction.

In this paper, we presented a new design of x-ray fluorescence CT imaging system. For detecting fuorescence signals of gold nanoparticles in-vivo, multiple spectroscopic detectors are arranged and rotated orthogonal to an excited region of interest so that a localized scan can be acquired with a maximized efficiency. Excitation filtration was employed to minimize the effects of low-energy x-rays and background scattering for lowering radiation dose to the object. Numerical simulations showed that the radiation dose is less than 300 mGy/second for a complete 30 views tomographic scan; and the sensitivity of 3D fluorescence signal detection is up to 0.2% contrast concentrations of nanoparticles. The x-ray fluorescence computed tomography is an important molecular imaging tool. It can be used directly in samall animal research. It has great translational potential for future clinical applications.

Dynamic bowtie for fan-beam CT.

A bowtie is a filter used to shape an x-ray beam and equalize its flux reaching different detector channels. For development of spectral CT with energy discriminating photon-counting (EDPC) detectors, here we propose and evaluate a dynamic bowtie for performance optimization based on a patient model or a scout scan. With a mechanical rotation of a dynamic bowtie and an adaptive adjustment of an x-ray source flux, an x-ray beam intensity profile can be modulated. First, a mathematical model for dynamic bowtie filtering is established for an elliptical section in fan-beam geometry, and the contour of the optimal bowtie is derived. Then, numerical simulation is performed to compare the performance of the dynamic bowtie in the cases of an ideal phantom and a realistic cross-section relative to the counterparts without any bowtie and with a fixed bowtie respectively. Our dynamic bowtie can equalize the expected numbers of photons in the case of an ideal phantom. In practical cases, our dynamic bowtie can effectively reduce the dynamic range of detected signals inside the field of view. Although our design is optimized for an elliptical phantom, the resultant dynamic bowtie can be applied to a real fan-beam scan if the underlying cross-section can be approximated as an ellipse. Furthermore, our design methodology can be applied to specify an optimized dynamic bowtie for any cross-section of a patient, preferably using rapid prototyping technology.